Quetzalcoatl was a South American Aztec god. This causes one very strong problems for critics trying to claim that the Jesus story borrowed from the Quetzalcoatl story. How do they suppose the Israelites heard about Quetzalcoatl? Yet another problem is that many historians believe that the Quetzalcoatl stories sprang up in the Americas around the 10th century A.D., roughly 900 years after Jesus walked the Earth. Another serious problem for the critics here is that almost everything we know about Quetzalcoatl comes from documents written after Europeans started visiting the Americas. Since the Europeans were there to spread the Christian religion, it's likely that the religion of Quetzalcoatl would have absorbed much Christian influence, making any similarities between Jesus and Quetzalcoatl most likely the result of Christian influence on Quetzalcoatl, not the other way around.
Critics are fond of pointing out that Quetzalcoatl was a white man. When Cortez arrived, the Mesoamericans apparently thought that he was Quetzalcoatl returning to them. However, it should be noted that Jesus was not white, but Jewish. Some critics claim that Quetzalcoatl also wore a white robe like Jesus, but the only references to Quetzalcoatl's clothing refer to a cloak with green feathers. Quetzalcoatl's mother was Coatlicue, and in some versions of the legend she was a virgin somehow impregnanted by a ball of feathers. But again, his 'virgin-born' status likely arose from Christian influence. Another similarity that critics point to is that Quetzalcoatl was tempted as Jesus was. There's no indication that this story predates Columbus, and, besides, in Quetzalcoatl tradition, he gives into his temptations, committing incest and getting drunk.
All things considered, the idea that the Jesus stories borrowed from the Quetzalcoatl stories is one of the least likely to be valid.