As was mentioned earlier, the understanding that Jesus Christ is both 100% human AND 100% God was settled by the Church at the Council of Chalcedon in 451 AD. This truth is called the "hypostatic union." Jesus has two natures in one Person. He is both fully Divine and fully human. Every view that denies this truth since that time in Church history has been deemed heresy by ALL of the three divisions of "Christendom," Protestantism, Roman Catholicism and Eastern Orthodox.
Jesus was conceived of the Virgin Mary, without human father. He got his human nature from his mother ("the seed of the woman"). When He was tempted, He was tempted as a human. That He was God did not make Him any less human, or any less susceptible to the temptations that humans fall heir to.
As to the tricky question, "COULD Jesus have sinned?" Someone started another thread somewhere today about being "comfortable with paradoxes." This is a case where we have a paradox in which we, as finite, limited human beings cannot reason nor rationalize the answer. The answer is yes -- and no. In His humanity He was heir to the weaknesses of the flesh, and His temptations were real and threatening. But as God, He could not be tempted -- at least not successfully.
We tend not to like paradoxes. That's especially true of theologians. In this case, however, we have to accept the mystery of the "God/Man," and of how He could/could not sin. I'll wait on Him to explain that to me when I go to be with Him. No one on this board -- or on this earth -- can adequately reveal all this truth entails.
JDale