Rep. Michele Bachmann enjoyed a day of lucrative fundraising, national media exposure and glowing analysis of her newfound momentum on Tuesday, following a strong performance in her first presidential debate.

She also forced her competitors to assess how she might affect their own paths to the Republican nomination.

“She did a great job of weaving in her experiences as a foster mother, a congresswoman and an attorney,” said GOP strategist Ron Bonjean, who is not affiliated with any contender. “The other candidates are now forced to personalize their stories more. I think this is just surprising — how well she did — and that was really noticed.”

Since she first floated the idea of running for president, Bachmann has been lumped in with some of the more fringe characters in the contest, in part the result of her short time on the national stage and her uncompromising views.

By turning in a confident and savvy performance, the Minnesotan at least temporarily carved a spot as a serious candidate — one whose presence will almost certainly affect the race no matter how far she goes.

The most immediate effect Bachmann will have is in Iowa, where she was born and where she could hold particular appeal among the social conservatives who dominate the first-in-the-nation caucuses.

A viable Bachmann campaign would be a particular threat to former Minnesota governor Tim Pawlenty, who has pinned his hopes on winning in Iowa to establish himself as the leading alternative to former Massachusetts governor Mitt Romney, the front-runner, who is focusing on New Hampshire.

Pawlenty demurred when asked in a TV interview at a campaign stop Tuesday to comment on Bachmann’s entrance into the race, and Romney, saying only, “I thought she did a very nice job.”

If she is able to build on her momentum, her influence could widen considerably. Hugely popular with the tea party movement, Bachmann could siphon conservative votes from other GOP contenders. Her no-compromise positions on such issues as the nation’s debt ceiling (she doesn’t want it raised) could force the rest of the field to follow suit. She could rally women to action, and her cachet as an energetic, straight-talking conservative could make it more difficult for former Alaska governor Sarah Palin to find a path into the field.

“I look forward to bringing the voice of the common sense of the American people that I’ve brought to the halls of Congress, to the tea party, now to the White House, where it’s been missing for far too long,” Bachmann said Tuesday on CBS’s “Early Show,” one of numerous TV interviews she gave.

Her candidacy “keeps the tea party voters engaged,” said Leslie Sanchez, a GOP strategist and the author of “You’ve Come a Long Way, Maybe,” a book about women in politics. “Especially early in the primary, they know that they have the voice and someone who’s challenging the status quo.”

But Bachmann also faces a challenge as she looks to broaden support beyond tea partyers, who embrace her because of the inflammatory rhetoric and unflinchingly conservative stances that have made her a controversial figure to others, including some within the GOP.

She has called President Obama “anti-American” and a socialist, and recently declined to answer when a reporter asked whether she considers homosexuality a public health hazard. Earlier this year, she positioned herself to the right of her Republican colleagues in the House when she delivered the tea party response to Obama’s State of the Union Address — even though Rep. Paul Ryan (Wis.) was already on tap to make the official Republican rebuttal.

In Monday’s debate, she declined to say whether she supports abortion in cases of rape and incest. And she has called climate change a hoax.

“The most important thing in my mind is defeating Barack Obama,” said Tom Molloy, 66, a retiree from Brentwood, N.H., who attended Bachmann’s debate-viewing party at a restaurant in Manchester, but who has not committed to her. Molloy said he thought Bachmann’s performance showed “a passion for running for president,” but added that he wonders whether she can broaden her appeal enough to compete against Obama.

Bachmann seemed aware of her challenge to expand her reach onstage Monday at Saint Anselm College in New Hampshire. She repeatedly spoke of her accomplishments as a member of Congress and her experience pushing the limited-government agenda that has earned her a passionate following nationwide.

“I was the very first member of Congress to introduce the full-scale repeal of Obamacare,” Bachmann said early in the debate.

At another point, she said: “I’ve already voted ‘no’ on raising the debt ceiling in the past. And unless there are serious cuts, I can’t.”

Bachmann’s rhetoric regularly morphed into the sort of zippy and exuberant proclamations that have made her a darling of the tea party rally circuit — but that don’t necessarily earn the confidence of voters looking for a president.

“When Americans go in to vote or hold their hand up in a caucus, they’re thinking to themselves, ‘Can I visualize this person sitting in that office?’ ” said Rich Galen, a GOP consultant who is unaffiliated in the nomination contest. “When someone is engaged in rah-rah campaign rhetoric like that, for a lot of people like me, I cannot visualize her as president of the United States.”

Teri Christoph, a founder of Smart Girl Politics, an online network of about 40,000 conservative women, said Bachmann made an impression.

“Palin supporters are hard-core, but I think some of the other grass-roots folks who like Palin but aren’t such die-hard fans are taking a second look at Bachmann now,” Christoph said. “She seemed very serious. I think some of the criticism toward her is that she’s a little flaky, but she stayed on message.”

Bachmann fully committed to running for president on Tuesday, when she said she will suspend her campaign for a fourth term in Congress. And her pollster, Ed Goeas, said the still-forming team, which includes campaign manager Ed Rollins and former Mike Huckabee communications chief Alice Stewart, spent most of Tuesday hunkered down and figuring out how to take advantage of Bachmann’s momentum.

“That’s what we’re all kind of tied up with right now,” Goeas said. “We spent half the day just reading the press, which is a good thing — a very good thing.”