Well we know that Jesus was fully man. Men have the ability to sin
We also know that Jesus was fully God. God does NOT have the ability to sin due to the fact that he is... God :)
So we have a dilemma here (no DUH) While I'm not brilliant enough to tell you how Jesus can be both full man and fully God here is how I look at the question of whether Jesus could sin.
If we look at Matt 4 we see Jesus in the wilderness being tempted by Satan. So to be tempted you have to have the ability to succumb to that temptation otherwise it wouldn't be a temptation. (Think about it)
Also in Is 50:5 (This is Jesus prophesying about himself) "The Sovereign LORD has opened my ears, and I have not been rebellious"
So we know that He had the opportunity to rebel (disobey) the Father. But didn't
So I think that while Jesus had the ability to sin, but Chose not to. This is something that should be a great comfort to us. We have to remember that:
"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." 1Cor 10:13