It was only last month that Texas Governor Rick Perry decided to enter the race for the Republican Party's presidential nomination and quickly zoomed to the top of public opinion polls. But in recent weeks Perry has stumbled in the candidate debates, and the new doubts about Perry have led some Republicans to renew pressure on New Jersey Governor Chris Christie to enter the race.

The first actual votes in the U.S. presidential nominating process are still months away, but it has already been a roller-coaster ride for Rick Perry.

Perry came into the race as a favorite among Christian conservative voters who also boasts a strong record of job-creation in Texas.

"America is going to be guided by some set of values," said Perry. "The question is going to be whose values and I would suggest most of the people in this audience believe it is those Christian values that this country was based upon."

But Perry has stumbled in recent debates, both in trying to attack his main rival, former Massachusetts governor Mitt Romney, and in trying to defend his record as Texas governor.

Perry has also been criticized by conservative rivals for supporting a Texas law that allows the children of illegal immigrants to qualify for in-state university tuition rates.

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.

"Republicans are so excited about the possibility of Christie getting into the race. I have not seen anything like this in my time in politics," noted Luntz.

Political analysts say Governor Perry must show improvement in upcoming debates or risk losing his frontrunner status.

David Gergen has served as an aide to Republican and Democratic presidents and teaches at the Kennedy School of Government at Harvard University.

"How long he will stay there we don't know," said Gergen. "It is unclear whether Governor Perry of Texas is a rising star or a shooting star and we will have to wait and see how the next few months go."

Perry still leads Romney in the latest CNN-ORC poll by a margin of 28 to 21 percent, but Perry's support is down slightly from the same poll two weeks ago.