I've heard the phrase, "God will never ask you to do anything you can't do," far too many times in my life. In fact, I have probably said it before myself. That may be because people are actually referring to 1 Corinthians 10:13, that says, "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." Even then we often forget the part where it says He will provide a way of escape.
As I listened to a speaker today on the radio, he made the point that God does in fact ask us to do things we cannot do. Case in point, would be the story of "The Woman at the Well." It's a fairly well known story of where Jesus interacts with a Samaritan woman and goes against all sorts of "rules," but just speaking to her. What I have never paid much attention to before, however, was the fact that He asked her to go get her husband, when He knew she didn't have a husband. He asked her to do something she couldn't do.
As I began to think about it, I think about the things I feel like God has been asking me to do, that seem like things I can't do. I have to believe that God sometimes asks us to do things in our lives that we can't do, because He knows our heart and wants to use that question to point out an area in our life where there is something we can't do on our own, but rather He has to do it for us. It is a point of our lives that we have to submit to Him because He is the only one that can.
Take for instance, the "Rich Young Ruler," who asked Jesus what it would take to gain eternal life. When Jesus listed off all the commands and the ruler said that he had done those things since he was a child, Jesus said, ok, God sell everything you have and give it to the needy. First, there was no way that man had kept all of those rules since he was a child. No one is perfect, but even if he was speaking of the fact that he had been forgiven by God, the point was that he was still looking for what HE could do to EARN his way into heaven. Jesus told him to do something that he "couldn't" do, while trying to help him realize it had nothing to do with his works, but rather in came through Jesus himself.
So really, its somewhat of a two fold thought. One, Christ does ask us to do things we can't do. Two, asking us to do something we can't do helps us realize we have no hope outside Jesus.