Cornyn also said that he doesn't believe the GOP should use the term RINO.
"If I found someone who agreed with me nine times out of ten, I'd be working with them all I could. I wouldn't be calling them names," he said. "That's not a recipe for success. So you can count me in when it comes to stopping the name-calling; that’s really the lazy person's substitute for thoughtful discussion and debate."
Cornyn said that the differences between the establishment Republican party and the Tea Party are about messaging, not policy.
"As it turns out, most of the differences are about tone and style; they are not about policy. Even the most recent debate over the government shutdown and the effort to defund Obamacare was about tactics, not about goals," Cornyn said, adding that explaining his governing style "seems to address most if not all of the concerns that voters have in the primary."
Cornyn also addressed a tweet he published in November that indicated he thought that the White House pushed for a nuclear deal with Iran in order to distract from the botched Obamacare rollout.
"Notice that I didn't mention Iran there. Now, there's no question I was thinking in part about that, but I was also thinking about Benghazi, the IRS and Syria. I do think the president has been very skillful at changing the subject whenever there's bad news," he said. "I will not mislead you and say that I wasn't thinking about Iran, but it was just one element."