Jesus said he didn't come to abolish the law. Instead Jesus says in Mt 5:48 "Be perfect, therefore, as your heavenly Father is perfect", and I don't think Jesus was joking. And this expectation of Jesus that we become perfect makes fully sense when you think about it. Jesus himself was fully human, like you and me, and it says of him that Jesus was tempted in every way we are tempted in as well.
The reason why Jesus never sinned, why he resisted all the temptations, is because he was in such a deep, close relationship with his Father in heaven. A relationship like we should be aiming for, because that close of a relationship with God is possible for us now indeed. That's what Jesus died for! To enable us to have this same relationship with the living God.
This might sound quite theoretical, but I found it to be true over the years. The more I was willing to obey God the more He guided me and enabled me through His spirit to resist temptations. Over time God did exactly what the Bible talks about - He forms me more and more into the image of His son.
There is still a few things I struggle with, but it got much much less compared to a few years ago, and I am certain that this "perfectness" Jesus talks about in Mt 5 is to be taken literally. It is possible! But you will only know that it is possible when you try it yourself, when you stop saying "nobody is perfect" and give all of yourself to God - when you let Him do the work in you He will do it.