Perry finished a disappointing second in a recent straw poll, or test vote, in Florida behind the surprise winner, Georgia businessman Herman Cain.

Cain told NBC's

Today

program that Perry's weak debate performances have raised questions among Republican voters as to whether he would be the strongest nominee against President Barack Obama in next year's election.

"I believe it hurt him a lot, not just in terms of what he said but in terms of how he said it," said Cain.

Other prominent Republicans are also raising questions about Perry's debate performances, including former Arkansas governor Mike Huckabee, who finished second to John McCain in the 2008 race for the Republican Party nomination.

"I think Rick Perry is not prepared for the pressure of the presidential stage yet," said Huckabee.

Some Republicans are concerned enough that they are urging New Jersey Governor Chris Christie to rethink his decision not to run for president.

Christie's blunt-spoken style is popular with Republican voters. But earlier this year Christie said he was not interested in running next year and so far there has been little public indication that he is willing to change his mind.

"I don't feel ready in my heart to be president," said Christie. "And unless I do, I don't have any right offering myself to the people of this country."

Republican pollster Frank Luntz says many Republicans would like to see Christie run for president.