If Ted Cruz wins (extremely unlikely) the Republican nominations the problem is going to be whether he is even eligible to run for presidency. It is going to be based on the interpretation of the law on what a native born citizen is. There is one place it is mentioned that there is an exception that allows someone born abroad to U.S. Parents to be a naturally born citizen. The key here though is that it says US Parents, parents plural.
Ted Cruz's father was a Cuban exile that at first helped out Castro and his mother is a US Citizen. They were in Canada for work and gave birth to Cruz there. His mom filled out the paperwork that made him a Canadian Citizen. According to the law on wedlock births with a US Woman and Alien Father, as long as they were married he gets a US Citizenship at birth. They would have to look at the marriage records though.