(CNN) -- Minnesota Rep. Michele Bachmann's newly official presidential bid drew fresh eyes Tuesday after complimentary reviews of her performance in a face-off with her Republican rivals.

Several CNN analysts declared her one of the winners of the CNN-sponsored New Hampshire GOP debate Monday night, while House Speaker John Boehner said the third-term congresswoman "did a really good job last night."

"I think she is a bright member of our caucus," Boehner told reporters. "It's one of the reasons why I appointed her to the Intelligence Committee."

During her relatively short time in Washington, Bachmann has staked out a position on the far right and made some gaffes that have made her the butt of critics' jokes. She has accused Obama of forcing "tyranny" on Americans, earning CNN contributor John Avlon's "Wingnut of the Year" award in 2009. She has been complimented as the next Sarah Palin and dismissed as "a poor man's Sarah Palin," as Meghan McCain, the tart-tongued daughter of the 2008 GOP presidential nominee, put it in February.

But underestimating Bachmann would be a mistake, University of Minnesota political science professor Larry Jacobs said.

"She's very strategically smart," Jacobs said. "Michele Bachmann has taken on the political establishment throughout her career and has prevailed each time."

Bachmann played down the plaudits in a Tuesday interview on CNN's "American Morning."

"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," she said. "So that was really my focus last night."

Bachmann is the sole woman in the current seven-member GOP field, running at 4% in a CNN-Opinion Research Corp. poll taken last week. Front-running former Massachusetts Gov. Mitt Romney drew 24% in that survey, while Palin, who has not announced whether she will run, got 20%.

But Bachmann told CNN her campaign is "just out of the box."

"I think that now we'll be able to make our case to the American people," she said. "And I think that we'll see then an increased level of support around the country."

During the debate, she touted her sponsorship of bills that would repeal two of the Obama administration's biggest congressional wins: the health care law and the Dodd-Frank overhaul of Wall Street regulations that passed following the 2008 financial collapse. And she called for cuts in corporate taxes and a rollback of what she called "job-killing" environmental regulations, steps she told CNN would revive the staggering American economy "in a quarter or two."

Bachmann, 55, was born Michele Marie Amble in Waterloo, Iowa, a fact she naturally is playing up in that early caucus state. She was raised a Democrat as she grew up in various cities across the Midwest, and met her husband, Marcus, while working on Jimmy Carter's 1976 presidential campaign. She switched parties in 1980, attracted by Ronald Reagan's anti-abortion platform.

She has an education degree from Minnesota's Winona State University, went on to earn a law degree from Oral Roberts University in Oklahoma and studied tax law at the College of William and Mary in Virginia. She worked as an attorney for the Treasury Department in the 1990s, arguing civil and criminal tax cases. The couple has raised five children and helped raise 23 foster kids.

She placed the foster children in public school and, unhappy with what they were learning, ultimately ran for a seat on the school board. She lost that race, but left an impression on at least one rival.

"The Michele Bachmann that people see today is the same one as 15 or 20 years ago. She engages them. She energizes them. She's an evangelist. By that I mean she inspires people to act," said Mary Cecconi, who sat on the Stillwater, Minnesota school board, and said she and Bachmann didn't always see eye to eye on issues.

Cecconi said Bachmann was against same-sex marriage and spoke in favor of teaching creationism.

"I don't think there's been a tremendous evolution," she added.

Bachmann went on to challenge a moderate Republican incumbent in a 2000 campaign for the state Senate. Few thought she would have any chance, but she succeeded.

"She won because of her organizational skill and her understanding of where she could build a base of support, particularly through churches and other conservative organizations in the district," Jacobs said.

During her six years in St. Paul, Bachmann was the "furthest out you could get" on the social conservative spectrum, Jacobs said.

"She was the one introducing legislation that other Republicans were shy about signing on to," he said.

Bachmann says God encouraged her to run for higher office. She won her suburban Minneapolis-St. Paul seat in Congress in 2006, becoming the first Republican woman to represent Minnesota.

She first drew national attention in 2008, when she attacked what she called Obama's "anti-American" associations and suggested during an MSNBC interview that news organizations should investigate which other members of Congress were "pro-America or anti-America."

She has railed against Obama's economic policies, comparing them variously to Marxism and slavery, and once suggested Obama's push for volunteer service would lead young Americans into "re-education camps." She announced in 2009 that she would fill out only basic family information on her forms for the upcoming census, warning that the Obama administration could not be trusted to protect personal data. GOP colleagues publicly prodded her to reconsider, noting that the 2010 survey would be used to apportion federal funds and draw congressional districts.

In 2010, she became the chairwoman of the newly formed Tea Party Caucus in the House of Representatives. But Monday night, when a longtime New Hampshire Republican official expressed concern that the Tea Party movement would drive away moderate Republicans and independent voters, Bachmann said all elements of the GOP are needed in a "three-legged stool."

"We need the peace-through-strength Republicans, we need the fiscal conservatives, we need the social conservatives," she said. "We need everybody to come together, because we're going to win. Just make no mistake about it."

In April, 2008 GOP runner-up Mike Huckabee's former political director signed onto Bachmann's campaign. The same month, she edged out Huckabee -- who isn't running in 2012 -- in a straw poll at Liberty University, the Virginia college founded by onetime Moral Majority leader Jerry Falwell.

Jacobs said Bachmann has the building blocks needed for a successful presidential campaign: money, an enthusiastic base and a distinguishing set of policy ideas.

"There are some serious assets for her to run, and I think the tendency to dismiss her is just not in touch with the hardcore reality of her kind of political balance sheet," he said.

CNN's Chris Welch contributed to this report.