Republicans focused on House and Senate races are growing anxious that former Speaker Newt Gingrich might win the GOP presidential nomination.

These Republicans, including Members and party operatives, tend to believe former Massachusetts Gov. Mitt Romney would give the GOP its best chance to hold the House and flip the Senate in 2012. And for the moment, they still predict Romney will win the nomination.

But for the first time, there is real concern that Gingrich could defeat Romney in Florida on Jan. 31 and ride that momentum to victory in the states ahead, despite Romney’s organizational advantage.

Sen. John McCain, a Romney backer who is headed to Florida later this week to campaign for the former governor, conceded that the battle with Gingrich is competitive. The Arizona Republican described Romney’s double-digit loss to Gingrich in South Carolina as a “significant setback. You can’t paint it any other way.” But McCain said he was encouraged by Romney’s feisty debate performance Monday night.

“I think he’s still going to win, but it’s going to be much tougher. I mean, it’s very obvious,” said McCain, the GOP’s 2008 presidential nominee. “I think most people believe that Newt Gingrich cannot win a general election — among other things. And some people are alarmed at the prospect of sending out U.S. Marshals to round up federal judges when they do things that the legislative branch or executive branch may disagree with.”

McCain was referring to a Gingrich proposal to hold federal judges more accountable for their decisions by compelling judges to testify before Congress. The former Speaker has also indicated support for making it easier to remove judges from the bench and possibly eliminating circuit courts.

After badly losing in Iowa and New Hampshire, Gingrich surged to the lead in Florida and nationally on the strength of his first-place finish in South Carolina and two strong debate performances in the run-up to Saturday’s election. He now leads Romney by 7.4 points in Florida and by 1.3 points nationally, according to the latest RealClearPolitics average. However, many Republicans expect the vote in Florida to be close.

Gingrich, historically a conservative firebrand, has moved to position himself to the right of Romney on key issues. But Sen. Jim DeMint, who has not endorsed in the race and expects the volatile GOP primary to last well past Florida, suggested that the race between Gingrich and Romney has nothing to do with who is more conservative.

“I’m really not sure it’s about who’s the most conservative. It may be about who’s the most assertive,” said DeMint, a stalwart conservative and tea party favorite. “When I go around the country, people don’t thank me for being the most conservative, they just say, ‘Thanks for fighting.’”

The South Carolina Republican, cautioning he still thinks the race could take another turn, dissected the Gingrich-Romney battle this way:

“Mitt’s kind of had a low-risk strategy; Newt had nothing to lose, in effect, and threw it all out,” he said. “What Newt did, whether it was planned or accidental, he took on the CNN, took on John King — who I don’t think often gives us a fair shake — and people like that. At the same time Mitt’s allowed himself to be positioned as the establishment candidate when in fact he’s the only one who hasn’t been in Washington.”

Republican strategists who believe Romney gives the GOP its best chance to succeed up and down the ticket, in conservative and swing states, are beginning to worry about the possibility of a Gingrich victory in the primary, although they are not panicking.

Fresh polls show that Romney’s personal unfavorable ratings have sunk nearly as low as those of Gingrich, which have been stuck at above 50 percent since the beginning of the race. But the view among most is that Romney has room to recover and that Gingrich’s image is too defined and entrenched to change.

“For the first time people are thinking Newt could beat Romney, which is scaring people to death. Mitt has to win Florida or he will be consumed,” said one Republican operative who focuses on Congressional races.

However, a prominent Romney backer expressed confidence that the governor would ultimately win the nomination.

“I’m very confident that Gov. Romney is going to get the nomination,” Sen. Kelly Ayotte (R-N.H.) said. “He’s working very, very hard. And, as with any election there are always ups and downs. But he has built a national campaign that is prepared to go the distance.”