Is it easy to live a Christian life?

Karl Barth answers this question quite well in a piece he wrote called The Call of Discipleship. He says that the gospel is not easy to live by, but that if we will not take upon ourselves the yoke (the teaching of Jesus) we will wear a yoke 10,000 times heavier, the world's.

I doubt any apostle would have said it is easy. Not even Jesus:

Luke 22:43-44 ESV And there appeared to him an angel from heaven, strengthening him. And being in an agony he prayed more earnestly; and his sweat became like great drops of blood falling down to the ground.

But is it PEACEFUL? Well that depends!

John 16:33 ESV I have said these things to you, that in me you may have peace. In the world you will have tribulation. But take heart; I have overcome the world.

2 Corinthians 12:9-10 ESV But he said to me, “My grace is sufficient for you, for my power is made perfect in weakness.” Therefore I will boast all the more gladly of my weaknesses, so that the power of Christ may rest upon me. For the sake of Christ, then, I am content with weaknesses, insults, hardships, persecutions, and calamities. For when I am weak, then I am strong.

We will have troubles and suffering, etc... but it's up to us to find our peace in our Savior. Our eternity is secure in him no matter what troubles come. When we lose sight of that our troubles can seem overwhelming. But when we know our eternity is secure then we can find true contentment.

No, it is not easy; it is completely impossible:

Matthew 5:48

Be perfect, therefore, as your heavenly Father is perfect.

That's the Gospel's standard, according to Jesus.

So, what should we do? As David Stratton's answer states, even Paul had this problem. However (following on from the verses David quotes) Romans 8 answers this.

1. First, we're not under condemnation for not achieving this standard (Romans 8:1).
2. We can actually be set free from sin and helped by God to get ever closer to perfection (Romans 8:9).

For the record, the whole chapter is worth a read...

I do not believe that the verses cited mean that it is easy to live a Godly life, and to abstain from sin simply because we're saved. No less than Paul himself, who wrote a good portion of the New Testament struggled against his sin nature. He wrote about it often, but I think that the most raw and honest writing, which dealt directly with his struggle is found in Romans 7. (Quoted from the KJV)

15 For that which I do I know not: for what I would, that do I not; but what I hate, that do I.

16 If then I do that which I would not, I consent unto the law that it is good.

17 Now then it is no more I that do it, but sin that dwells in me.

18 For I know that in me (that is, in my flesh,) dwells no good thing: for to will is present with me; but how to perform that which is good I find not.

19 For the good that I would I do not: but the evil which I would not, that I do.

20 Now if I do that which I would not, it is no more I that do it, but sin that dwells in me.

21 I find then a law, that, when I would do good, evil is present with me.

22 For I delight in the law of God after the inward man:

23 But I see another law in my members, warring against the law of my mind, and bringing me into captivity to the law of sin which is in my members.

24 O wretched man that I am! who shall deliver me from the body of this death?

25 I thank God through Jesus Christ our Lord. So then with the mind I myself serve the law of God; but with the flesh the law of sin.

In summary, Paul is saying "I want to do good, but I don't do it, and I HATE it!" (verse 15). Then he goes on to tell about how in his flesh, his earthly nature, there is no good thing, but he also delights in the Law of the Lord, and there is a war going on inside him, constantly, with his flesh warring against his spirit.

If Paul, who was willing to suffer imprisonment, torture, and death for the cause of Christ had problems living Godly, then who are we to expect to just sail through it?

In my personal life, I can answer this way (admitting up front that this is subjective, and personal). I had a lot of things in my life that were sinful. I won't list them here, but there was a list. I didn't give them up immediately when I was saved, and when I tried to give them up under my own power, using my own willpower and determination, I was unable to escape the bondage of my sins.

Eventually, I learned how to simply give up and ask God to make the changes in me. Being a proud, stubborn, willfull person, this was a very hard lesson to learn. But the truth is, once I asked God to take away my desire to do certain things, He did it. Not immediately, but He did.

Taking just one example, I was into p**nography from the time I was 15 or so. Giving that up, especially with the Internet at my fingertips was difficult. Like Paul, I knew what it was like to want to live one way, but keep getting sucked into sin. It was like quicksand with tentacles that reaches out and grabs you. Finally, I learned to give up and stop trying to do it under my own power, and just gave it over to Him, asking Him to remove the desire, and as I said, He did.

When I read about the load being light, and finding rest, I think about that struggle and others like it. Once I turned it over to Him, it was easy, and the internal warring eventually ceased. He took away the desire, so that I was no longer sucked in as easily. I learned to flee temptation immediately, get on my knees and pray for help.

This is infinitely easier than doing it on my own. His spirit is able, while I am in submission to Him, to take away the temptation and allow me to see sin as God sees it - wretched and vile, which removes the temptation completely. The load is lightened, and it is easier than struggling on my own. To me, that is what those verses mean.

These people are likely thinking of verses like these:

John 15:18-20 (NIV)

    ¹⁸ “If the world hates you, keep in mind that it hated me first. ¹⁹ If you belonged to the world, it would love you as its own. As it is, you do not belong to the world, but I have chosen you out of the world. That is why the world hates you. ²⁰ Remember what I told you: ‘A servant is not greater than his master.’ If they persecuted me, they will persecute you also. If they obeyed my teaching, they will obey yours also.

Matthew 5:10 (NIV)

¹⁰ Blessed are those who are persecuted because of righteousness,
   for theirs is the kingdom of heaven.

Rightousness and persecution are linked together in these two. However, there is a verse that makes the link explicit:

2 Timothy 3:12 (NIV)

¹² In fact, everyone who wants to live a godly life in Christ Jesus will be persecuted,

The verses you referenced talk about interaction between God and Christians, but if you say something like "following Christ's Gospel (being righteous) makes life easy", then people will assume you mean the interaction between Christians and the world, which is indeed not an easy life.