(CNN) -- Republican presidential hopefuls sought to turn their performances in Monday night's debate into campaign fuel Tuesday, whether by declaring victory or explaining how they had approached one of the earliest tests of their political strength.
The Barack Obama re-election campaign, meanwhile, wasted no time striking back at the seven contenders who spent much of the evening bashing the president.
While a survey of GOP insiders, the National Journal Political Insiders poll, found that former Massachusetts Governor Mitt Romney was the biggest winner of the debate in New Hampshire, two other campaigns issued statements declaring their candidates had won.
"Newt Gingrich clearly won the debate," said Joseph DeSanits, spokesman for the former house speaker's presidential effort. "He cut through the clutter and spoke clearly. His message resonates. Newt decisively addressed the challenges facing the nation, the destructiveness of the Obama administration, and offered an optimistic vision for America's future."
A senior adviser to former Senator Rick Santorum of Pennsylvania issued a statement saying Santorum had "again" proven himself "strongest to take on Obama."
"While some on the stage tonight preferred to give one-sentence applause lines, Senator Santorum concentrated on giving direct, honest answers that offered not just criticisms of the current administration but real solutions to address our nation's most serious challenges," John Brabender said in the statement.
The CNN/WMUR/New Hampshire Union Leader debate took place in the first state to hold a presidential primary. Results in New Hampshire -- like those in Iowa, which holds its caucuses before New Hampshire's primary -- set a tone for the entire race.
The National Journal Political Insiders poll found 51% saying front-runner Romney won the debate, 21% citing Rep. Michele Bachmann of Minnesota, and 9% saying Pawlenty had won.
Meanwhile, 26% said Pawlenty was the biggest loser of the debate.
Asked about that by CNN on Tuesday morning, Pawlenty acknowledged that "people may have been expecting an attack on Mitt Romney."
In the debate, Pawlenty avoided a chance to repeat the criticism of Romney he had introduced the day before. On a Sunday political talk show, Pawlenty had tied Obama's health care law to Romney's health care law in Massachusetts, using the word "Obamneycare."
When pressed during the debate, Pawlenty declined to repeat the phrase.
He told CNN's "American Morning" on Tuesday that he felt he was repeating the same point he had previously made, "which is President Obama was the one who indicated he used the Massachusetts health care plan as the blue print for Obamacare, so it was restated essentially the same way."
Numerous analysts say Pawlenty missed an opportunity to take a swipe at the front-runner. Asked whether he felt he missed an opportunity, he told CNN "the debate was focused primarily on Barack Obama and his failure as president."
While Bachmann won plaudits for her performance in the debate, she told CNN on Tuesday, "I wasn't thinking about performance. I was really just thinking about President Obama and what we can do to make sure that he is a one-term president, because frankly, he hasn't done a great job serving the interests of the American people."
Robert Gibbs, the president's former spokesman who is now a surrogate for his re-election campaign, told CNN, "I think you saw last night that Republicans wanted to spend more time trying to bash the president than talking about their own records." Gibbs took aim at Romney's record on job creation and Pawlenty's on his state budget.
"I think what you saw last night were candidates espousing the very same ideas that got us into a financial, a fiscal, and an economic mess a few years ago," Gibbs said Tuesday morning.
The two other presidential hopefuls in the debate were Rep. Ron Paul of Texas and businessman-turned-talk show host Herman Cain.
Not all the expected candidates for the Republican presidential nomination took part in the debate, so the full roster for Obama's competition remains unclear.
A CNN/Opinion Research Corp. survey released Monday before the debate showed Romney is the choice of 24% of Republicans and independents who lean toward the GOP. Former Alaska Gov. Sarah Palin came in second at 20%, followed by former New York Mayor Rudy Giuliani and the rest of the field.
Palin and Giuliani, who have not announced that they will join the race, did not participate in Monday's CNN/WMUR/New Hampshire Union Leader debate.
Jon Huntsman, the former governor of Utah who resigned to serve as Obama's ambassador to China, plans to enter the race as well.
"It's hard at this point to be worried about one specific person," Gibbs said. "I will say that, judging by everything that we see, you can tell that this Republican nomination is at its most unsettled that we've seen it in quite some time."