Sweeping aside much of the intraparty noise that has dominated the Republican presidential race in recent days, voters in the primary here on Tuesday appeared to be united behind a single goal: defeating President Obama and a set of policies that have driven them into a rage.

Debbie Finch was among the angry voters. Finch, 39, said she never liked Obama much. She voted for Hillary Rodham Clinton in the Democratic primary in 2008, then for Republican John McCain in the general election.

But after three years of the Obama presidency, Finch is motivated by a desire to oust him in November. And so she was among the many who voted for former Massachusetts governor Mitt Romney on Tuesday, calculating that he has the best chance in the general election.

“I just want Obama out. It’s about jobs and money, and I’ve seen my income go down since Obama took office,” Finch said. “I did like Ron Paul, but I had to look at the general. Romney can tap into Obama’s base. The others are too far right.”

Echoing a line from Romney’s stump speech, Finch said: “I think Obama is a good person but in over his head.”

In a state known for its independent and engaged civic participants, that sentiment was surprisingly uniform, helping catapult Romney to victory. More than eight in 10 voters said they were “angry” or “dissatisfied” with the Obama administration’s policies, according to exit polls. And as Republicans and unaffiliated voters decided the outcome of the nation’s first primary of 2012, there were signs of potential general-election trouble for Obama, who won the state in 2008 by nearly 10 percentage points, in part because of his cross-party appeal.

More independents participated in this New Hampshire primary than in previous years, early exit polling showed. Some, such as Susan Riggs, 77, a retired nursing assistant, supported Obama in 2008. She said she would back any Republican except Romney to defeat Obama, who she said has “been on vacation for the last three years.” In the end, Riggs chose Jon Huntsman Jr., a former governor of Utah, who came in third place, saying he “came across as being sincere.”

“I like his international experience,” Riggs said. “I’m just tired of Romney.”

Exhaustion was another theme. Although there was a crush of activity in the final days before the voting — including two debates in 12 hours over the weekend — campaigning had been underway for years, with Romney banking on a victory in the state next door to his home base of Massachusetts. The long campaign seemed to work against Romney with some voters.

“They started so early,” said Elaine Cote, 39, a legal assistant who decided some time ago to support Huntsman. “It feels like this has been going on for two years. This one was ahead and then that one. It was all over the place.”

Perhaps that contributed to the indecision: About one in five reported that they still hadn’t made up their minds heading into primary day, an extraordinary figure given how familiar they had become with the candidates after so much retail politicking. It drove morning talk-radio hosts here crazy. Could voters really have been paying that much attention, they wondered on-air, if so many still had not picked a candidate?

In fact, many voters said they were engrossed in the campaign, torn between imperfect candidates with competing assets.

Ray Scott, 68, was among those surprised by his own indecision. “Boy, it’s been a tough year,” he said.

The retired salesman said he was undecided even as he made his way to his polling place in Goffstown. He had thought about supporting former House speaker Newt Gingrich (Ga.), who he said is “brilliant” and would know how to get things done in Washington.

But then doubt crept in. Was Gingrich too close to Washington? “He’s such an insider,” Scott said. Then he went through the rest of the candidates. Romney, Huntsman — both admirable but with too little elected experience. Former senator Rick Santorum (Pa.), whom he liked but could not get behind “because I don’t think Santorum can beat Obama,” Scott said.

Finally, he made a choice: Rep. Ron Paul (Tex.), who came in second place. “I went with the guy with the good message.” Moments later, he said he felt good about it. “I’m comfortable right now,” he said, pausing.

“Very comfortable?” he continued. “No.”

Dave Fish, 57, a retired United Parcel Service worker from Bedford, struggled with a similar bout of uncertainty. He expressed what few Republicans have: satisfaction with the field.

But he had to make a choice, and in the end, it was about electability.

“I just feel like Romney is the best candidate to go against Obama,” he said. “I was leaning toward Newt and recently looking at Huntsman. But Romney has been working at this for six years, and I think he can get the job done.”

Staff writer Rosalind S. Helderman in New Hampshire contributed to this report.