Harwood: The first president of your adulthood was a Texan, George H. W. Bush. What is your evaluation of his presidency now?
Cruz: I think he did an effective job when it came to managing the demise of the Soviet Union. He was the right person at the right time. Domestically, I disagree with what he did. When you tell the American people, "Read my lips. No new taxes," that should mean no new taxes. That was a mistake. And it's a mistake that cost him the election.
Read MoreSen. Ted Cruz blames the media for distorting his image
Harwood: You worked for his son. Was he right to expand Medicare to cover prescription drugs?
Cruz: That was a policy fight I was not engaged in at the time. I'll tell you what wasn't right. When George W. Bush entered office, the national debt was $5 trillion. When he left, it was $10 trillion. I think the administration spent too much money. Now, I also think you've got to give George W. Bush some real credit—he showed remarkable courage in the beginning of the second term taking on Social Security reform and personal accounts. It was the right thing to do. Sadly, congressional Republicans ran to the hills and abandoned him.
Harwood: A third Texas president, L.B.J., created Medicare in the mid-'60s. Your hero Ronald Reagan campaigned vigorously against that, saying it would lead to socialized medicine, would end liberty in the United States. Who was right: L.B.J. or Reagan?
Cruz: It's not worth tilting at windmills. I don't know. I wasn't alive then. What I do know is that today, we have got to preserve and reform Medicare. There is a broad, universal consensus that Medicare is a fundamental bulwark of our society. Look, it's one thing to have asked 50 years ago should we have created it. It's another thing when you have a generation of seniors who paid into it 30, 40, 50 years who have been made promises. We need to honor those promises.
Harwood: You announced your campaign at Liberty University. You're appealing to Libertarians. The Libertarian Party platform in 2012 calls for Social Security to be phased out. Are they wrong as a matter of philosophy?
Cruz: Oh, I understand why they call for that. But I don't agree with them. What I would like to see is several things. Number one, for those on Social Security or near retirement, no changes whatsoever. Honor the commitments. But for younger people, people in my generation, we should gradually increase the retirement age. Secondly we need to change the rate of growth of Social Security benefits so they match inflation rather than exceed inflation. Those two reforms on their own take Social Security from bankruptcy into solvency. But the third piece, and it's what Bush fought for, is personal accounts. I think it is transformative to allow younger workers to put a portion of their taxes into a personal account that they own, that they control, and that they can pass onto their heirs.
Harwood: I read an anecdote that said you asked a friend at Harvard Law School her IQ, and then when she didn't know her IQ, asked her SAT score. What was that about?
Cruz: That was a silly story that appeared in a magazine. I have no recollection of ever having had any such conversation. So, I can't respond.