Perry lost a key test vote in Florida to businessman Herman Cain on Saturday after making a strong effort to win. Perry's second-place finish in the straw poll came just days after he faltered in a debate in Orlando, Fla.
Perry's recent troubles have sparked another round of angst among Republicans about their slate of presidential candidates.
In an interview with the Associated Press Saturday after he had left Florida for a lunchtime speech in Michigan, Perry addressed speculation that New Jersey Gov. Chris Christie might reconsider running for president in 2012.
"I see anybody that gets in the race that believes in America and is a small government but efficient government individual, I would welcome into the race. It just strengthens the point that the Republican Party's all about getting our country working again. Whoever that is," Perry said of Christie. "And I'm also a big believe in these governors being freed up to be able to compete against each other. Chris Christie is a great competitor - and I'll be up there, you know, in Jersey, looking for some businesses to move to Texas."
Christie insisted just this Thursday that he does not plan to run for president in 2012. Bill Palatucci, Christie's longtime friend and political adviser, told the AP on Saturday night, "Nothing has changed."
But the more intense discussions of a Christie candidacy are further evidence that Perry's bid could be in trouble.
Activists at the Florida test vote kept bringing Christie up as a possible contender. Merick Lewin, who owns a marketing company in Davie, Fla., said he believes it's a two-person race - unless Christie runs.
"He's tough. He's strong. He could really shake this up, especially if Rick Perry implodes," Lewin said.
Perry, a late entrant into the Republican primary who quickly led national polls, stumbled in recent weeks.
His defense of in-state tuition rates for illegal immigrants put him on the wrong side of the GOP's conservative base. His rivals worked to exploit his opposition to a fence along the U.S.-Mexican border and his support of a mandatory vaccine for girls against a sexually transmitted disease.
Perry left Florida to speak to GOP activists at a gathering on Mackinac Island in Michigan. Romney, the son of a former Michigan governor, also was attending that event.
Cain captured 37.1 percent of the vote at Saturday's Presidency 5 straw poll in Orlando, with Perry coming in second with 15.4 percent. Mitt Romney came in third with14 percent and former U.S. Sen. Rick Santorum of Pennsylvania followed with 10.88 percent.
While all declared candidates were on the ballot, the first-tier candidates did not compete. Perry bought hundreds of activists' breakfasts on the sidelines before heading to Michigan. Romney skipped and didn't send representatives to the forum. Romney and U.S. Rep. Michele Bachmann of Minnesota both left Florida before the voting began and their campaigns discounted the straw poll's role in the campaign. Bachmann finished eighth with 1.51 percent in the straw poll.
The results were unlikely to shuffle the campaign's standings. Instead, they were mostly a popularity contest among the delegates selected by local party organizations.
Ahead of the test vote, Perry's campaign bought breakfast for hundreds of the party faithful assembled for a three-day conference and debate. Perry said skipping the straw poll was a blunder.
"I think that's a big mistake. I think it's very important," Perry said, citing its history.
Previous straw polls have predicted the GOP nominee.
Ronald Reagan won in 1979, George H.W. Bush in 1987 and Kansas Sen. Bob Dole in 1995. The Republican Party of Florida, however, has not organized the test vote in recent years.
After the vote, Perry released a statement congratulating Cain. His spokesman, Mark Miner, acknowledged his debate performance played a role in the straw poll vote, but insisted the campaign would not change strategy.
"He's the commander in chief, not the debater in chief," Miner said.
Cain's speech Saturday energized the attending activists. "Let's send Washington a message: We the people are still in charge of this country. Not we, the bureaucrats. Not we, the government," Cain told the conference.
Santorum said delegates should stand with "someone who can win the election, someone who is a consistent, authentic conservative ... who has proved they can win in states that we have to win."
Former U.S. House Speaker Newt Gingrich said he was the one who could best take on Obama.
Hunt reported from Mackinac Island, Mich. Associated Press reporter Beth DeFalco contributed to this story from New Jersey.