Former Florida Gov. Jeb Bush was second, with 15 percent of those surveyed. New Jersey Gov. Chris Christie and Kentucky Sen. Rand Paul both were chosen by 11 percent, Wisconsin Rep. Paul Ryan 9 percent, Texas Gov. Rick Perry was sixth with 7 percent and Florida Sen. Marco Rubio only got 6 percent.

When each candidate was paired against potential Democratic candidate Hillary Clinton, the poll showed some candidates might be in for a tough race. Cruz would beat Clinton 49 percent to 44 percent, the survey found, and Clinton would beat Perry 48 percent to 44 percent.