CNN

McCain said Tuesday the immigration bill does not propose an amnesty policy.

WASHINGTON (CNN) - Notably missing from President Bush's meeting with Capitol Hill Republicans to discuss immigration reform Tuesday, Arizona Sen. John McCain addressed the hot button issue of amnesty while on the campaign trail in California.

"I think that amnesty means forgiveness. Amnesty means any past infraction that you have committed, then is forgiven. This is a very serious punishment," McCain said. He added, "You're paying a heavy penalty. That's like saying, if you're guilty of a traffic violation and you go and pay the fine, then you're getting amnesty. That doesn't fit my definition."

McCain's unwavering support for immigration reform isn't popular with conservatives, and his unrelenting support for the war in Iraq isn't popular with the majority of Americans. But McCain said he's happy about where he stands among his Republican rivals in recent polls.

"The polls bounce around a lot. We're happy with where we are now and how we're doing," McCain said. "And it's tough. It's a tough campaign, and I understand how strongly people feel on immigration, how people feel on some of the issues that I've been in the arena on."

McCain also said he'd welcome actor and former Tennessee Sen. Fred Thompson into the race.

"He's a very attractive man. And maybe there's an argument that he should be president. He's been president two or three times before," McCain said. "I understand that Fred's a very attractive and articulate guy, so I say, come on in, the water's fine."

– CNN Associate Producer Lauren Kornreich