What if we were not tempted by the devil but rather, we failed God's test?

The question isn't really if you'll fail, but rather when you'll fail. "For all have sinned and fall short of the glory of God."

Simply put, what becomes of you depends on whether you belong to Christ or not. It's not who tempts you that makes any difference, it's that you (and I, and everyone) are sinful through and through, and we will, at some point, fail, making ourselves a failure in God's eyes. (Incidentally, that's what James 1:14, the next verse says... we're lured not by God, not by Satan, but by our own desires.)

The fact that we're all going to fail is what Jesus is for. He sacrificed for us, so that when we do fail, we can rest in the fact that his sacrifice paid any penalty we might owe to pay for the failure we've done.

Sorry to keep it so short and sweet, but I think a simple question deserves a simple answer. If you're Christ's, then eternally, you'll be with Him. If you're not, then you aren't.

You get more tests until you die. If the scripture is not wrong in saying, 'He wills that all men be saved," what happens when you fail God's tests which everything is, even evils, since while he does not tempt you himself he permits the temptation (it would not happen if he did not allow it) is that he keeps training you and pruning you. We are told this process does not actually end at death, but that the saints continue to increase in perfection eternally.

God is interested in our spiritual development so that we be made perfect in the likeness of his Son Jesus Christ. If we fail in a test assigned by God, we will have to undergo the same test after some time. This continues till we pass that particular test. Please look at the Following Scriptures.

JEREMIAH 18:1-6 "The word which came to Jeremiah from the Lord, saying: 2 “Arise and go down to the potter’s house, and there I will cause you to hear My words.” 3 Then I went down to the potter’s house, and there he was, making something at the wheel. 4 And the vessel that he made of clay was marred in the hand of the potter; so he made it again into another vessel, as it seemed good to the potter to make. 5 Then the word of the Lord came to me, saying: 6 “O house of Israel, can I not do with you as this potter?” says the Lord. “Look, as the clay is in the potter’s hand, so are you in My hand, O house of Israel!"

Satan's purpose of a Temptation is to Destroy us. But God will never allow his evil designs to succeed.

Scripture says that God will never give us more to bear than we can and that he will always provide a way out. From our experience, that's surely been true although we admit that sometimes we think God thinks we can bear more than we think we can. He is always right about that, too.

Beloved, God tests us to refine us and consecrate us for him in order that we may be closer to him, and that God may be glorified in us.

And I will bring the third part through the fire, and will refine them as silver is refined and will test them as gold is tested. They will call on My name, and I will hear and answer them. I will say, It is My people; and they will say, The Lord is my God.
Zec 13:9

God, like a good Father, will not let us fall too far into a hopeless state through his trials. Take money, for example. If we covet money, God will not bless us financially. He will do what is necessary to show us that we need to surrender this part of our lives to Him, to refine us of this covetous desire, but will not, for example, let us fall into a severe hopeless state of poverty, i.e. something that we are not capable of handling or escaping.

For no temptation (no trial regarded as enticing to sin), [no matter how it comes or where it leads] has overtaken you and laid hold on you that is not common to man [that is, no temptation or trial has come to you that is beyond human resistance and that is not adjusted and adapted and belonging to human experience, and such as man can bear]. But God is faithful [to His Word and to His compassionate nature], and He [can be trusted] not to let you be tempted and tried and assayed beyond your ability and strength of resistance and power to endure, but with the temptation He will [always] also provide the way out (the means of escape to a landing place), that you may be capable and strong and powerful to bear up under it patiently.
1 Cor 10:13 -- See also NIV translation

The difference in being led astray by the devil in his temptation is a blurry line for me, so sorry if this is not correct (please correct me), but there is a difference. When we give ourselves over to sin, and do not heed to God's conviction and repent, we fall away from God. But if we are truly God's and have real faith in him, we should not intentionally do this. I believe these kinds of people are defined in Matthew 13:7&22:

Other seeds fell among thorns, and the thorns grew up and choked them out.
Matt 13:7
As for what was sown among thorns, this is he who hears the Word, but the cares of the world and the pleasure and delight and glamour and deceitfulness of riches choke and suffocate the Word, and it yields no fruit.
Matt 13:22

Given the text, these people are probably not truly God's. But only God knows.

But the gate is narrow (contracted by pressure) and the way is straitened and compressed that leads away to life, and few are those who find it.
Beware of false prophets, who come to you dressed as sheep, but inside they are devouring wolves.
You will fully recognize them by their fruits. Do people pick grapes from thorns, or figs from thistles?
Even so, every healthy (sound) tree bears good fruit [worthy of admiration], but the sickly (decaying, worthless) tree bears bad (worthless) fruit.
Matt 7:14-17

Sin

• First, it is important to understand that God desires intimate, loving relationship with His people and between His people. The whole law is built upon this.

"And [Jesus] said to him, '"YOU SHALL LOVE THE LORD YOUR GOD..." This is the great and foremost commandment. The second is like it, "YOU SHALL LOVE YOUR NEIGHBOR..." On these two commandments depend the whole Law and the Prophets.'” (Matthew 22:37-40, NASB)

"...therefore love is the fulfillment of the law." (from Romans 13:10, NASB)

• The law was given to illustrate righteous (loving) behavior, and sin is any deviation from that.

"...I would not have come to know sin except through the Law; for I would not have known about coveting if the Law had not said, 'YOU SHALL NOT COVET.'" (from Romans 7:7, NASB)

"for until the Law sin was in the world, but sin is not imputed when there is no law. " (from Romans 5:13, NASB)

"Everyone who practices sin also practices lawlessness; and sin is lawlessness." (1 John 3:4, NASB)

Temptation

• In the context of James 1:13 (the passage you were asking about), we also learn what the definition of "temptation" is. Another way of saying "he tempted me" is to say "he enticed me to follow my lust into sin."

"...one is tempted when he is carried away and enticed by his own lust. Then when lust has conceived, it gives birth to sin..." (from James 1:14-15, NASB)

• In light of that definition, it is ludicrous to think that God would tempt us, because that would be the same as saying "God was enticing me to follow my lust and disobey His law." Of course, God would not do this, as James 1:13 explains.

• Satan on the other hand is definitely interested in enticing us to follow our lust into sinful disobedience. But our great, loving God will be right there at our side, helping us in these times of need, and showing us the way through.

"No temptation has overtaken you but such as is common to man; and God is faithful, who will not allow you to be tempted beyond what you are able, but with the temptation will provide the way of escape also, so that you will be able to endure it." (1 Corinthians 10:13, NASB)

God Does Test Us

• A "test" is where God places you in a challenging situation to reveal your heart condition. A test can reveal such things as whether a person will trust Him, or walk in love, or obey His commandment.

"...the LORD your God has led you in the wilderness these forty years, that He might humble you, testing you, to know what was in your heart, whether you would keep His commandments or not." (from Deuteronomy 8:2, NASB)

"...the LORD your God is testing you to find out if you love the LORD your God..." (from Deuteronomy 13:3, NASB)

What If We Fail?

• A test is an opportunity. If we "pass" the test, it is an opportunity for glory and reward, and to be a good witness to others.

"...you have been distressed by various trials, so that the proof of your faith, being more precious than gold which is perishable, even though tested by fire, may be found to result in praise and glory and honor at the revelation of Jesus Christ..." (from 1 Peter 1:6-7, NASB)

• If we "fail" the test, it is an opportunity to learn something about our hearts and grow in our relationship with the Lord. There isn't a person on the planet who doesn't occasionally "fail", but God is merciful toward those who belong to Him. As the saying goes, "God is the God of a second chance"... or as I heard one Pastor say, "God is the God of another chance".

"My little children, I am writing these things to you so that you may not sin. And if anyone sins, we have an Advocate with the Father, Jesus Christ the righteous" (1 John 2:1, NASB)

"For we all stumble in many ways..." (from James 3:2, NASB)

"Therefore, confess your sins to one another, and pray for one another so that you may be healed..." (from James 5:16, NASB)

• It is interesting that you asked what would have happened if Abraham had failed his test. I think it is helpful to understand that in a way, he did! God promised him a son and he wanted it so bad that he decided to try to make it happen on his own with his servant rather than trusting God. But he got it right eventually, and that's what he is now remembered for, by the grace and love of God.