(CNN) -- GOP presidential candidate and Texas Sen. Ted Cruz locked horns in an interview with "Late Show" host Stephen Colbert in front of a charged audience on Monday night. The conversation was a surprising mix of humor and substance, with the two debating the legacy of Ronald Reagan, the need for compromise in government and gay marriage -- while also finding time to invoke Donald Trump and discuss the rigors of campaigns.
Colbert kept the first half of the interview lighthearted, joking about the size of the GOP field and life as a presidential candidate. Asked, "What are the days like?" Cruz cracked, "You just have to surgically disconnect your shame sensor because you spend every waking moment asking people for money."
Though Cruz was also quick to emphasize his enthusiasm for the campaign, the exchange lead to some early sparks between the host and the candidate. When Cruz described himself as "a kid in a candy store" on the campaign trail, Colbert fired back, "Who's paying for the candy?" winking at the deregulation of campaign finance prompted by the Supreme Court's Citizens United decision, and garnering big applause from the studio audience.
The discussion then turned to -- where else -- GOP frontrunner Donald Trump. With Trump set to appear on "The Late Show" the following night, Colbert asked Cruz if he had any questions he'd like him to ask the business mogul. The Texas senator joked, "If you could, ask him if he would possibly consider donating $1 billion to our campaign."
The real verbal fireworks came after a break, however, when Colbert asked Cruz -- one of the more conservative GOP candidates, and a favorite of the Tea Party movement -- about his ability to work with Democrats and progressives should he become president.
He challenged, "Convince the people out there who are not far right why you should be someone they should consider to vote for should you get the nomination."
Cruz responded by highlighting Ronald Reagan's success attracting Democratic voters, arguing that it was his ideas, and not his willingness to compromise, that won over liberals.
"Those Democrats didn't come over because Reagan was the squishiest middle of the road candidate -- they came over because he represented principles that were appealing," he offered.
Colbert then noted that Reagan supported a number of policies and principles that are anathema to modern conservatives, in particular a tax increase and amnesty for illegal immigrants, and asked Cruz, "Are those aspects of Reagan something you could agree with? Raising taxes and amnesty for illegal immigrants?"
The GOP presidential candidate replied, "No, of course not."
The two continued the debate, with Cruz contending that "Ronald Reagan also signed the largest tax cut in history" and Colbert returning, "But when conditions changed in the country, he reversed his world's largest tax cut and raised taxes when revenues did not match the expectations."
"So it is a matter of compromising," Colbert added, before asking again about compromise and joking, "Would you believe that it's important not to call the other side the devil?"
Cruz agreed, saying "When others attack me, I make a point on keeping the focus on substance." He went on, "What I am fighting for are simple principles -- live within our means, stop bankrupting our kids and grandkids, follow the Constitution."
Colbert seized on Cruz's statement, quipping "And no gay marriage."
With that, the debate turned to the constitutionality of the Supreme Court's ruling in favor of gay marriage rights. Cruz argued "Under the Constitution, marriage is a question for the states, if you want to change the marriage law." He pointed to the 10th Amendment, which enshrines the principle of federalism whereby states make laws concerning questions and powers not addressed in the Constitution.
Colbert, however, pressed Cruz, saying "I'm asking what you want."
Cruz replied, "I believe in democracy. I believe in democracy and I don't think we should --," before he was cut off by boos from the disapproving audience. But "The Late Show" host unexpectedly reprimanded the crowd, insisting "No, no, guys, guys, however you feel, he's my guest, so please don't boo him."
Cruz wrapped up his argument by criticizing the Supreme Court, saying "I don't think we should entrust governing our society to five unelected lawyers in Washington." He added, "If you want to win an issue, go to the ballot box and win at the ballot box. That's the way the Constitution was designed."
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