Jim Cole, File, Associated Press
FILE - In this June 13, 2011 file photo, Republican presidential candidate, former House Speaker Newt Gingrich and former Massachusetts Gov. Mitt Romney participate in a presidential debate at St. Anselm College in Manchester, N.H.
We've had many occasions to debate together and we'll have more, I presume quite a few more, before this is finished.

BETHLEHEM, N.H. — Republican presidential candidate Mitt Romney on Thursday spurned chief rival Newt Gingrich's challenge for a one-on-one debate in the run up to the Jan. 3 Iowa caucuses but dismissed the notion — suggested by the former House speaker — that he was afraid to participate in such a face-off.

"We've had many occasions to debate together and we'll have more, I presume quite a few more, before this is finished," Romney told The Associated Press. "But I'm not going to narrow this down to a two-person race while there are still a number of other candidates that are viable, important candidates in the race. I want to show respect to them."

Gingrich was campaigning Thursday in Virginia, the day after inviting Romney to debate him and discuss negative TV ads that Romney's allies are running in Iowa. Gingrich focused largely on Obama at his first stop but had several events planned throughout the day.

In a brief interview aboard his campaign bus as it rumbled through New Hampshire, Romney reflected on the GOP nomination fight that's seen many candidates and non-candidates rise and fall in the polls. He mentioned Gingrich, Minnesota Rep. Michele Bachmann, Atlanta businessman Herman Cain, Texas Gov. Rick Perry and real estate magnate Donald Trump.

Asked whether Trump and Gingrich were of equal seriousness as presidential aspirants, Romney said: "I'm not going to get into that. It's up to you to make your own assessment."

The former Massachusetts governor also distanced himself anew from the standoff in Washington between the GOP-controlled House and the Democratic-run White House over a two-month extension of a cut in payroll taxes.

"I really don't think it's productive for me to describe which of all of the compromises within the sausage-making process is my favorite compromise position," Romney said, adding that presidential candidates getting involved will only complicate the process, not help it.

"We have, what, eight people running for president?" Romney said. "The idea of us all running to Washington and trying to say to the various parties, 'Here's where I think you should go,' is not something which our party needs, it is not likely to be conducive to reaching a conclusion."

He added: "We're in the last few days before the Iowa caucuses and I'm not going to leave my campaign, fly to Washington and spend a couple of weeks there negotiating something where there are already people elected to do that very job, that we expect to do so."

It was an implied reference to GOP presidential nominee John McCain shutting down his campaign in fall 2008 during the financial crisis.

For weeks, Romney has refused to be pinned down on how Congress should break an impasse that threatens to raise taxes for 160 million workers — the latest pressing policy debate he has sidestepped. House Republicans have rejected a bipartisan compromise in the Senate that would have kept the tax cuts going for two months, and called instead for negotiations toward a one-year extension of the reduction.

But Romney has left open the terms for an extension. He has suggested it should last more than two months and ideally a year, but has said such details are "deep in the weeds."

Democrats are working to highlight how the tax cut affects people. A family making $50,000 a year would lose about $19 per week if the tax cut isn't extended. The White House has asked people to write in and say what the approximately $40 every two weeks means to them. Some have said it would pay for fresh produce instead of fast food, or new shoes.

What would Romney do with the $40? "Probably give it to my grandkids," he told the AP.

Romney said in the interview that, if elected, he would "sit down with the leaders in my party and the leaders in the opposition party and work to find some sort of common ground." He offered advice — and criticism — of the man he hopes to succeed, saying: "If the president would take a personal role in leading that process I think we'd have more prospects of it being successful."

Romney added: "It doesn't strike me that they're terribly far apart. I will be surprised if they can't get this resolved on a timely basis."

Gingrich, campaigning in Richmond, Va., blamed Obama, saying the president "is the primary reason" for the impasse over the payroll tax cut. He said a two-month extension "makes no sense," and that the political squabbling makes the U.S. look like Italy.

Gingrich focused nearly all his ire on Obama and went easy on his GOP rivals.

In his typically bombastic style, Gingrich said everything Obama "believes in kills jobs." He said "Obama has a European radical attitude toward class warfare" and is "the best food stamp president."

"I studied history, and unlike the president, I studied American history," Gingrich told about 200 Republicans at a breakfast, where a key goal was gathering the signatures needed to qualify him for Virginia's March 6 ballot.

Gingrich did not name any of his rivals during his 14-minute speech, but managed gentle swipes at Texas Rep. Ron Paul and Romney during a question-and-answer period.

Gingrich said he feels the threat of a nuclear-armed Iran is much graver than Paul does. He also said Romney's mandatory health insurance policy when he was Massachusetts governor will hurt him in New Hampshire.