New Jersey Gov. Chris Christie's (R) re-election Tuesday night didn't pass without a seeming slight from Sen. Rand Paul (R-KY), who described Christie as "a moderate" hours after he explicitly called himself a conservative.

"I think the Republican Party is a big party, and we need moderates like Chris Christie who can win in New Jersey," Paul told CNN host Wolf Blitzer. "What that means about the national party, I'm not sure there's an answer. But we do need moderates like Chris Christie in the party."

CNN noted that Christie made strong inroads with Black, Latino and women voters while defeating state Sen. Barbara Buono (D), both developments that could help him make the case to be the GOP's presidential candidate in 2016. But to do so, he would presumably have to challenge Paul and Sen. Ted Cruz (R-TX), both favorites among Tea Party conservatives.

"I think the party, in general, is more conservative," Paul told Blitzer. "I think there's room for moderates in the party. I think it will be more difficult. States like Iowa are very conservative. South Carolina is very conservative. New Hampshire, I think, is conservative with a little bit of a libertarian bent. It's a tough road, but I think we need ideas, and we need a broader party in many ways. I welcome him to the party, and I think he's an important part of it."

Earlier in the day, Christie told Blitzer's colleague Jake Tapper that he considered himself a conservative.

"I think that's [something] some people disagree with in our state," Christie said. "It's generally a left-of-center, blue state. But I think that the difference has been, I haven't tried to hide it, or mask it as something different. I just tell people, 'This is who I am.'"

Watch Paul's interview with Blitzer, as posted online on Tuesday, below.