LAS VEGAS (AP) — Herman Cain has risen fast. Now the question is: Will he fall?

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As Republican presidential hopefuls were preparing for a debate here Tuesday night, Cain has been facing more and more intense scrutiny as his poll numbers have jumped upward.

Now that he's in the national spotlight, he's already had to apologize for comments he made over the weekend calling for an electric fence on the Southern border with Mexico.

At a campaign stop Monday in Arizona, Cain appeared with Maricopa County Sheriff Joe Arpaio, an aggressive anti-immigration proponent. "It was a joke," Cain said emphatically during a news conference. "I apologize if I offended anyone. Mea culpa, mea culpa, mea culpa."

Cain told an audience in Tennessee on Saturday that the fence is "going to be electrified. And there is going to be a sign on the other side that says, 'It will kill you.'"

Immigration already has flared on the campaign trail — and contributed to the sinking of another fast-rising GOP candidate. Texas Gov. Rick Perry has struggled to explain why he signed a law giving in-state tuition breaks to illegal immigrants at Texas universities. When he first entered the race, he was at or near the top of many national polls. He's fallen back since, and Cain has emerged as the more popular alternative to former Massachusetts Gov. Mitt Romney.

Also participating in Tuesday's debate are Romney, Perry, Minnesota Rep. Michele Bachmann, Texas Rep. Ron Paul, former Pennsylvania Sen. Rick Santorum and former House Speaker Newt Gingrich.

Missing is former Utah Gov. Jon Huntsman, who's boycotting the Nevada caucuses in defense of New Hampshire's first-in-the-nation primary. Nevada has scheduled its contest for Jan. 14, and Republican officials are pressuring Romney and other Republicans to join Huntsman's boycott if the state refuses to hold the caucuses later in January.

Also potentially at issue on Tuesday is the foreclosure crisis. So far, it's been almost forgotten on the campaign trail, but the candidates will probably have little choice but to address it. Nevada has the nation's highest unemployment rate, a statistic that's driving the highest foreclosure rate in the nation. It's the root of the economic crisis, but it barely has been discussed as issues like immigration and vaccines for children have dominated the GOP primary.