Former Minnesota governor Tim Pawlenty wanted to start a fight with the Republican presidential front-runner, and on a Sunday talk show, he did — injecting into the 2012 sweepstakes a new term, “ObamneyCare,” that portrayed Mitt Romney’s Massachusetts health-care overhaul and President Obama’s federal law as one and the same.

But on Monday, standing next to Romney at a presidential debate, Pawlenty declined to stick with the fight. A wave of criticism ensued, and by Thursday, Pawlenty revived the attack to show that he’s got what it takes to go up against the two men — Romney and Obama — he sees standing between him and the White House.

The flare-up between the front-runner and the man hoping to be his main rival encapsulated the vulnerabilities of both — and the uncertainty among Republicans that either is equipped to go toe-to-toe against Obama.

In a wide-open presidential nominating contest, the GOP is more united than ever that its nominee must be ready for battle with Obama on health care as well as the economy. Some are uncertain that Romney is that man, given his role enacting an individual mandate in Massachusetts that Obama has said was a model for the federal overhaul that Republicans deride as “Obamacare.”

But by the end of the week, his indecision over how to attack Romney had combined with his uneven performance on stage to revive the very question Pawlenty had sought to dispel in going after Romney in the first place: Does he have what it takes to win?

“Everybody has always wondered if he is as vanilla as he looks,” said David Bossie, president of the conservative action group Citizens United. “There’s never been a question about Governor Pawlenty’s conservatism. But can he articulate a message?”

Pawlenty went at Romney with renewed vigor late Thursday in an interview with Sean Hannity, owning up to his “mistake” at the debate in not more forthrightly criticizing Romney and calling his rival a “co-conspirator” in the case against President Obama.

“I should have been much more clear during the debate, Sean,” Pawlenty said. “I don’t think we can have a nominee that was involved in the development and construction of Obamacare and then continues to defend it. And that was the question. I should have answered it directly.”

Pawlenty also sent this message out via Twitter: “On seizing debate opportunity re: healthcare: Me 0, Mitt 1. On doing healthcare reform the right way as governor: Me 1, Mitt 0.” And he repeated the tweet in a fundraising appeal sent out Friday morning.

Romney and his advisers, meanwhile, declined to comment publicly on Pawlenty’s attacks, instead staying focused on their message of jobs and the economy.

On Friday, just 10 hours after Pawlenty’s attack, the Romney campaign released a new web video that goes after President Obama over his handling of the nation’s unemployment. (The video also helped divert attention from a gaffe Romney made a day earlier in Tampa, where he jokingly told a small gathering of job seekers that he, too, was unemployed.)

Several Republicans close to Romney said privately they believe that responding to Pawlenty would only elevate a candidate who is otherwise mired in the single digits in most polls.

Others looked on with wonder at what Ed Rogers, a veteran GOP strategist who is close to Mississippi Gov. Haley Barbour, described as a “net loss” of a week for Pawlenty.

Pawlenty’s comments Thursday only reminded Republicans that “when he had the chance to be forthright and mano-a-mano with Romney, he took a pass, and when he’s behind his back he swung at him,” Rogers said. “The worst thing you do in politics is play to your negative stereotype. He has a negative stereotype that suggests he is a somewhat bland, mechanical politician and that’s he’s not great on his feet and he’s not unrehearsed. This reminded everybody of that.”

Some made the point that Pawlenty is right to go after Romney on an issue that is of paramount importance to activists. Herman Cain, the presidential contender and tea party favorite appearing Friday at the Republican Leadership Conference in New Orleans, said: “Let’s just say that it’s going to be tough, real tough,” for Romney to lead the battle against Obama on health care.

And Justin Sayfie, a top aide to former Florida governor Jeb Bush who is helping run Pawlenty’s campaign in Florida, said Republican donors and activists there and around the country are stirring for a fight over Romney’s health-care law.

Nonetheless, many Republicans cringed privately at the zigging and zagging that Pawlenty did this week. Pawlenty spokesman Alex Conant said the original “ObamneyCare” comment was intentional, and that the candidate’s only mistake was holding back at the debate. That doesn’t explain, however, why Pawlenty similarly held back at three other appearances in New Hampshire, nor why he waited 72 hours to regroup and burst forth once again.

Republicans also emphasized the peril of going negative so early in the nomination process — particularly for Pawlenty, who is unknown to many voters.

But most GOP leaders said the episode would be anything but decisive. Nearly all the contenders have one flaw or another that they’ve got to explain to voters. And the party is united behind defeating Obama, which means keeping an open mind about — and ultimately supporting — whoever winds up the Republican nominee.

“You know, the engines are just getting warmed up,” said former Republican National Committee chairman Ed Gillespie, also in New Orleans for the GOP conference. “All of the candidates are going to go through some bumps in the road. It’s a long process, and it’s a longer process this year than it’s been in a long time. We’re not likely to have a nominee til the first week of June. So there’s a lot of ground to cover between now and then.”

Staff writer Karen Tumulty and research editor Alice Crites contributed to this report.