What is the biblical argument against the claim that Jesus is just "a god", but not "God Almighty"?

The question in your title and the question in your post are technically asking two different things; I'll respond to the question in the title.

LDS doctrine holds that the Jehovah of the Old Testament is, in fact, Jesus Christ. Some evidence of this includes accounts that show that Christ created the Earth under the direction of the Father; see Hebrews 1:1-3 (KJV), among others:

1 God, who at sundry times and in divers manners spake in time past unto the fathers by the prophets,

2 Hath in these last days spoken unto us by his Son, whom he hath appointed heir of all things, by whom also he made the worlds;

3 Who being the brightness of his glory, and the express image of his person, and upholding all things by the word of his power, when he had by himself purged our sins, sat down on the right hand of the Majesty on high;

And His own pronouncement of His role as LORD; see John 8:58 (KJV):

58 Jesus said unto them, Verily, verily, I say unto you, Before Abraham was, I am.

Essentially, there is a difference between a god (an individual that has achieved exaltation, the highest blessing that the Father can bestow, of whom Jesus is one) and God (one of the numerous name-titles of the Ultimate Being in, and Almighty Ruler of, the Universe, the Father of our spirits).

The Gospel Principles manual goes into more detail for those that are curious.

To get to the answer, we can look first at whether there is any legitimacy to the claim that the Bible does teach that Jesus is "a god".

There are plenty of ways to interpret Scripture that might show Jesus as not being the God. Each of these either denies or ignores other verses that show that He is God, and therefore, deny or ignore the doctrine of the Trinity. These verses, taken out of context with the whole of Scripture could lead someone to believe that Jesus is not fully God.

One example:

Matthew 24:36 King James Bible (Cambridge Ed.)

But of that day and hour knoweth no man, no, not the angels of heaven, but my Father only.

Taken on its own, it seems to show that Jesus and the Father are not the same being. One knows something that the other does not.

The evidence against such a teaching is simply to look at the whole of Scripture and not ignore obvious claims that He is God. Such a claim is simply contrary to Scripture.

John 1 (KJV)

In the beginning was the Word, and the Word was with God, and the Word was God.

2 The same was in the beginning with God.

3 All things were made by him; and without him was not any thing made that was made.

4 In him was life; and the life was the light of men.

5 And the light shineth in darkness; and the darkness comprehended it not.

6 There was a man sent from God, whose name was John.

7 The same came for a witness, to bear witness of the Light, that all men through him might believe.

8 He was not that Light, but was sent to bear witness of that Light.

9 That was the true Light, which lighteth every man that cometh into the world.

10 He was in the world, and the world was made by him, and the world knew him not.

11 He came unto his own, and his own received him not.

12 But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name:

13 Which were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God.

14 And the Word was made flesh, and dwelt among us, (and we beheld his glory, the glory as of the only begotten of the Father,) full of grace and truth.

John 10:30 I and my Father are one.

His clear claim: http://www.gotquestions.org/I-AM.html

http://www.letusreason.org/trin16.htm

List of the I AM quotes from Jesus, showing that He is the I AM that spoke to Moses, from the link above:

John 6:51:"I am the living bread which came down from heaven. If anyone eats of this bread, he will live forever;"

John 8:23: And He said to them, "You are from beneath; I AM from above. You are of this world; I am not of this world.

John 8:12: Then Jesus spoke to them again, saying, "I AM the light of the world. He who follows Me shall not walk in darkness, but have the light of life."

John 8:58 Jesus said to them, "Most assuredly, I say to you, before Abraham was, I AM."

John 10:9: "I AM the door. If anyone enters by Me, he will be saved, and will go in and out and find pasture."

John 10:11: "I AM the good shepherd. The good shepherd gives His life for the sheep.

John 10:36: "do you say of Him whom the Father sanctified and sent into the world, 'You are blaspheming,' because I said, 'I am the Son of God'?

John 11:25: Jesus said to her, "I AM the resurrection and the life. He who believes in Me, though he may die, he shall live.

John 14:6: Jesus said to him, "I AM the way, the truth, and the life. No one comes to the Father except through Me.

John 15:1: "I AM the true vine, and My Father is the vinedresser.

John 19:2: Therefore the chief priests of the Jews said to Pilate, "Do not write, 'The King of the Jews,' but, 'He said, "I am the King of the Jews."'"

Acts 7:32: Stephen speaking of Moses' encounter at the burning bush "saying, 'I am the God of your fathers-- the God of Abraham, the God of Isaac, and the God of Jacob.' And Moses trembled and dared not look."

Acts 9:5: And he said, "Who are You, Lord?" And the Lord said, "I am Jesus, whom you are persecuting. It is hard for you to kick against the goads."

The I Am In the Old Testament was whatever man needed. He became, he was his all in all. Jesus in the New Testament uses all the examples to show who He is. He is everything to man and the only way to God.

The most important of all the statements is in John 8:24 after he tells them I am not of this world. "Therefore I said to you that you will die in your sins; for if you do not believe that I am [He], you will die in your sins." ( he is not in the original). He is communicating to them he is the same I AM that Moses met at the burning bush which commissioned him.

The idea that Jesus is a god comes from the claim that He IS God (Big "G", not a god - little "g") In other words, he is The God, the one and only, one of the three persons of the Trinity.

As far as saying that Jesus is a god , there are none. Nothing in Scripture says that Jesus is "a god". It doesn't say he is "a god", a teaching that would make him equal to Baal, or any of the other false "gods".

There may be, of course, those that believe such a thing, but it's not because it's found in the Bible.

For Jehovah's Witness - the primary advocate of the position that Jesus was merely a god, the primary proof text comes from the New World Translation of John 1:1. In this instance, the NWT says:

In beginning the Word was, and the Word was with God, and the Word was a god

In contrast, most mainline churches translate this:

In the beginning was the Word, and the Word was with God, and the Word was God.

Both Chalcedonian Christians and Jehovah's Witness agree that John 1:1 speaks of Jesus (John 1:14 makes this explicit). As such, this is a valid case.

Now, as to why Jehovah's Witnesses claim that this verse says the Word was a God, you do have to back to the Greek.

Ἐν ἀρχῇ ἦν ὁ λόγος, καὶ ὁ λόγος ἦν πρὸς τὸν θεόν, καὶ θεὸς ἦν [ὁ] λόγος.

The key question is whether or not the [ὁ] is legitimately definite ("the") or permissibly indefinite (could be "the" or "a"). The Net Bible says:

n Or “and what God was the Word was.” Colwell’s Rule is often invoked to support the translation of θεός (qeos) as definite (“God”) rather than indefinite (“a god”) here. However, Colwell’s Rule merely permits, but does not demand, that a predicate nominative ahead of an equative verb be translated as definite rather than indefinite. Furthermore, Colwell’s Rule did not deal with a third possibility, that the anarthrous predicate noun may have more of a qualitative nuance when placed ahead of the verb. A definite meaning for the term is reflected in the traditional rendering “the word was God.” From a technical standpoint, though, it is preferable to see a qualitative aspect to anarthrous θεός in John 1:1c (ExSyn 266-69). Translations like the NEB, REB, and Moffatt are helpful in capturing the sense in John 1:1c, that the Word was fully deity in essence (just as much God as God the Father). However, in contemporary English “the Word was divine” (Moffatt) does not quite catch the meaning since “divine” as a descriptive term is not used in contemporary English exclusively of God. The translation “what God was the Word was” is perhaps the most nuanced rendering, conveying that everything God was in essence, the Word was too. This points to unity of essence between the Father and the Son without equating the persons. However, in surveying a number of native speakers of English, some of whom had formal theological training and some of whom did not, the editors concluded that the fine distinctions indicated by “what God was the Word was” would not be understood by many contemporary readers. Thus the translation “the Word was fully God” was chosen because it is more likely to convey the meaning to the average English reader that the Logos (which “became flesh and took up residence among us” in John 1:14 and is thereafter identified in the Fourth Gospel as Jesus) is one in essence with God the Father. The previous phrase, “the Word was with God,” shows that the Logos is distinct in person from God the Father. sn And the Word was fully God. John’s theology consistently drives toward the conclusion that Jesus, the incarnate Word, is just as much God as God the Father. This can be seen, for example, in texts like John 10:30 (“The Father and I are one”), 17:11 (“so that they may be one just as we are one”), and 8:58 (“before Abraham came into existence, I am”). The construction in John 1:1c does not equate the Word with the person of God (this is ruled out by 1:1b, “the Word was with God”); rather it affirms that the Word and God are one in essence.

Basically, the sense is that the rest of John is pretty clear that Jesus was God - not a God, but this is the argument on which the NWT hinges.

The Alpha and Omega, the First and the Last, the Beginning and the End

Revelation 1 is probably the key passage the definitely asserts that Jesus is, in fact, God Almighty.

In Revelation 1:8, we have "the Almighty" introducing Himself in the conversation. The New World Translation identifies this as Jehovah.

“I am the Alpha and the Omega,” says the Lord God, “who is and who was and who is to come, the Almighty.” Revelation 1:8 ESV

“I am the Al′pha and the O‧me′ga,” says Jehovah God, “the One who is and who was and who is coming, the Almighty.” Revelation 1:8 NWT

Isaiah also speaks of Jehovah God as "the first and the last":

Thus says the Lord, the King of Israel and his Redeemer, the Lord of hosts: “I am the first and I am the last; besides me there is no god. Isaiah 44:6 ESV

“This is what Jehovah has said, the King of Israel and the Repurchaser of him, Jehovah of armies, ‘I am the first and I am the last, and besides me there is no God. Isaiah 44:6 NWT

So, the question is "Who is the Alpha and the Omega, the First and the Last?" The answer is conclusively that it is Jehovah God, the Almighty.

Jesus' as the First and the Last

After this, John hears a voice behind him. He turns to see someone "like a son of man", clothed with a long robe and with a golden sash around his chest, with hair as white as wool, with eyes like a flame of fire, feet on bronze, a voice like many waters, and a face shining like the sun. John faints when He sees this being, who lays His right hand on him and identifies as "the First and the Last", the living one, who died and is alive forevermore."

17 When I saw him, I fell at his feet as though dead. But he laid his right hand on me, saying, “Fear not, I am the first and the last, and the living one. I died, and behold I am alive forevermore, and I have the keys of Death and Hades. Revelation 1:17-18 ESV

And when I saw him, I fell as dead at his feet. And he laid his right hand upon me and said: “Do not be fearful. I am the First and the Last, and the living one; and I became dead, but, look! I am living forever and ever, and I have the keys of death and of Ha′des. Revelation 1:17-18 NWT

This is quite significant. The one claiming to be "The First and the Last", who is Jehovah God, the Almighty, claims to have died as well.

Jesus as the Alpha and the Omega

Finally, in Revelation 22, the Alpha and the Omega speaks again:

“Behold, I am coming soon, bringing my recompense with me, to repay each one for what he has done. 13 I am the Alpha and the Omega, the first and the last, the beginning and the end.”

Blessed are those who wash their robes, so that they may have the right to the tree of life and that they may enter the city by the gates. 15 Outside are the dogs and sorcerers and the sexually immoral and murderers and idolaters, and everyone who loves and practices falsehood.

“I, Jesus, have sent my angel to testify to you about these things for the churches. I am the root and the descendant of David, the bright morning star.” Revelation 22:12-16 ESV

“‘Look! I am coming quickly, and the reward I give is with me, to render to each one as his work is. I am the Al′pha and the O‧me′ga, the first and the last, the beginning and the end. Happy are those who wash their robes, that the authority [to go] to the trees of life may be theirs and that they may gain entrance into the city by its gates. Outside are the dogs and those who practice spiritism and the fornicators and the murderers and the idolaters and everyone liking and carrying on a lie.’

“‘I, Jesus, sent my angel to bear witness to ​YOU​ people of these things for the congregations. I am the root and the offspring of David, and the bright morning star.’” Revelation 22:12-16 NWT

Here, the Alpha and Omega, the First and the Last, the Beginning and the End, speaks, then identifies Himself as Jesus.

Conclusion

1. So, Jehovah God, the Almighty is identified as the Alpha and the Omega, the First and the Last, the Beginning and the End.

2. Then Jehovah God, the Almighty, asserts that He Himself has died. We know that it was Jesus who died.

3. Finally, the Alpha and the Omega identifies Himself as Jesus.

There are many arguments, but these are what I consider to be the greatest arguments against Arianism:

A "god" is a creature

A "god" (the lower-case "g" in English distinguishing the word "god" from "God" where the "G" is capitalized) indicates a created being, i.e. a creature.

Jesus is the "Word of God" (Rev. 19:13) and regarding the Word of God, it is written, "All things were made by him, and not one thing that was made was made without him" (John 1:3). In other words, Jesus created absolutely everything.

If Jesus is "a god,"

And "a god" is a creature,

But Jesus created all things,

Then the corollary is that something that had yet to be created must have created itself.

However, that is a logical impossibility. Something that does not exist cannot create itself.

Was God, ἄλογος?

The Greek word λόγος (logos) not only means "word," but also, "reason." It is written that Jesus is the Word of God who was with the Father in the beginning (John 1:1). However, if, as Arians assert, the λόγος of God (Jesus) was created, then the λόγος of God did not exist at one point. If the λόγος did not exist at one point, then one must admit that God was at one point ἄλογος (alogos), that is, "without reason," or simply, "irrational."

Scripture states that God created things in the beginning by His λόγος (Ps. 33:6 cp. John 1:3). But, how could God have created by His λόγος if indeed His λόγος did not exist yet? In fact, if God's λόγος is a creature, and God created all things by His λόγος (John 1:3), then how did God create His λόγος?

I only offer two or three arguments, but the early Church father's wrote tomes against Arianism.