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With Rick Perry's support dropping and Herman Cain's rising in GOP presidential race polls, Cain, a former pizza company executive who has mostly avoided attacking his Republican rivals, is now taking aim at the Texas governor.

Cain was the first Republican candidate to criticize Perry for leasing a Texas hunting camp with a racial slur in its name, a controversy sparked by a Washington Post report.

Even though Cain backed away from the criticism a day later, he has since held a book signing in College Station, Texas, home of Texas A&M University, Perry’s alma mater. And Cain told the National Journal Thursday that he would consider running as the vice presidential nominee for any of the candidates except Perry.

“Quite frankly, based upon Gov. Perry’s position on some issues, I would not be comfortable being his vice presidential nominee,” he said, noting Perry’s support for in-state college tuition for children of illegal immigrants and his opposition to a border fence.

It’s not clear whether Cain’s recent moves are part of a new strategy or if he simply doesn’t like Perry’s positions. Cain’s campaign did not respond to a request for comment for this story.

A batch of new polls show that Cain is on the rise apparently at the expense of Perry. A Fox News poll last week found that Cain's support nearly tripled to 17 percent while Perry fell 10 percentage points to 19 percent.

A CBS News poll this week also showed Cain increasing his support to 17 percent while Perry dropped from 11 percentage points to 12 percent. And in a Washington Post-ABC News poll this week, Cain gained 12 points and Perry lost 13 points, leaving both of them in a tie at 16 percent and trailing former Massachusetts Gov. Mitt Romney at 25 percent.

Political analysts told FoxNews.com that they expect Cain to step up his attacks on Perry in the next debate on Tuesday.

“The biggest problem Cain faces is he’s not well known among primary voters,” said David Hill, director of Hill Research Consultants. “The way you get better known is by taking on someone who is well known. … Better to attack the king than some unknown prince.”

Chris Begala, a political analyst and former adviser to President George H.W. Bush, said all of Perry’s supporters who have defected after the governor’s shaky debate performances have joined the Cain bandwagon. That alone will motivate Cain to keep attacking Perry.

“You go hunting where the ducks are,” he said.

He added that Perry knows he’s losing supporters to Cain, which will lead him to attack Cain, too. But Cain, he said, still has to prove he’s a serious candidate by raising money.

“I would just emphasize that Herman, I don’t think, is a flash in the pan,” he said. “He is a very serious front-running candidate.”

But Hill isn’t convinced, saying he sees a lot of things about Cain’s campaign that are amateurish and naïve. “Running for president requires many millions of dollars,” he said. “He’s a very smart political strategist, but the fact is he doesn’t have a lot of money. “

“Now, what he’s doing is admirable and the best one can expect to do with limited resources,” he added. “It’s sort of a guerrilla campaign, if you will, living off of what options you have. But that doesn’t make it a winning campaign.”

It’s not known how Perry will respond to Cain at Tuesday’s debate. Perry’s campaign did not respond to a request for comment. Begala said he would be surprised if the two didn’t exchange fire. But Hill would advise Perry to ignore Cain to avoid giving him more attention.

“The scenario today is Rick Perry and Mitt Romney as two tall trees on a plateau of stumps,” he said. “You don’t want to let one of those stumps sprout and become a third tree.”