Senator and Republican presidential candidate Ted Cruz, left, speaks with host Stephen Colbert on "The Late Show with Stephen Colbert." (Jeffrey R. Stabb/CBS via AP)

Sen. Ted Cruz (R-Tex.), like so many of the Republican presidential candidates, frequently evokes Ronald Reagan. But as Cruz talked about trying to bring in so-called "Reagan Democrats" to his campaign on the "Late Show with Stephen Colbert," the host wondered: how many of Reagan's policies would Cruz or other candidates agree with?

“Reagan raised taxes, okay. Reagan actually had an amnesty program for illegal immigrants. Neither of those things would allow Reagan to be elected today. So to what level can you truly emulate Ronald Reagan?” Colbert asked Cruz, who wants to lower taxes and is against amnesty. "Could you agree with Reagan on those two things?"

"No, of course not," Cruz said.

[Read: Republicans search for next Reagan, and 2016 hopefuls eagerly audition]

The exchange was part of a tough interview that touched on Reagan, gay marriage and, of course, Donald Trump.

Colbert told Cruz that when conditions changed Reagan "reversed his world’s largest tax cut and raised taxes when revenues did not match the expectations, so it’s a matter of compromising." Colbert asked if Cruz could compromise with the other side and not feel as though he "capitulated with the devil."

Cruz joked to Colbert that there is "nothing diabolical about you" and said he doesn't "respond in kind" when his opponents lob insults.

At one point, when talking about gay marriage, members of the audience started to boo Cruz.

"Guys, however you feel, he's my guest so please don't boo him," Colbert said.

The response capped an exchange where Cruz laid out the "simple principles" he espouses on the campaign trail: following the Constitution and reducing spending.

"And no gay marriage," Colbert said.

"Well actually, let’s be precise. Under the Constitution marriage is a question for the states," Cruz said.

"It doesn't mention marriage in the Constitution," Colbert said, and repeated it later. Cruz said that is why marriage is a question for states.

The Texas Republican said that he jokes with his seven-year-old daughter that running for president is simple.

"You just have to surgically disconnect your shame sensor because you spend every waking moment asking for money," he said. Cruz's campaign has raked in a lot — $14 million during the first and second quarter. Its allied Super PACs raised $38 million.

There is one more person Cruz would hit up for cash. When asked if Colbert could ask Trump, who will appear on the show Tuesday, anything on Cruz's behalf, the Texas Republican made it about money.

"I don't know if you know this but I'm told he's rich," Cruz, who has an unusually chummy relationship with Trump, said. "I like Donald a lot and if you could ask him if he could possibly consider donating $1 billion to our campaign."