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“We all know she is a huge proponent of getting back to the constitutional values, small government, and she understands spending is out of control,” said Jack Kimball, state GOP chairman. “I think the message she is putting out is resonating.”

Her debate performance and surge in the polls have led to speculation that she can be the “anyone-but-Romney” candidate, taking over the mantle of the hard-line conservative in the race.

The Democratic National Committee has not taken the same interest in Mrs. Bachmann that it has in Mr. Romney, but media scrutiny is increasing — particularly on questions about how the clinic her husband runs in Minnesota treats gay patients.

Her GOP opponents are beginning to take shots at her experience. Former Minnesota Gov. Tim Pawlenty, on NBC’s “Meet the Press” last weekend, called her record of accomplishment in Congress “nonexistent.”

“The downside for someone in the legislative body is that it’s hard to discern what kind of executive leadership skills they bring to the office,” said Ovide Lamontagne, a conservative powerbroker in the state who is flirting with a gubernatorial bid next year.

Mrs. Bachmann faces other challenges, too. She is trying to break through the glass ceiling to become the first female Republican nominee, and to become the first House member to jump directly into the White House since James A. Garfield pulled off the feat in 1880.

Joe McQuaid, the influential publisher of the Manchester Union Leader, called Mrs. Bachmann a “strong” and “attractive” candidate, but predicted that if Texas Gov. Rick Perry enters the race, he’ll be the conservative alternative next year.

“Unless Gov. Perry is a real dud, I think he is going to get a lot of that conservative action that is non-Romney,” Mr. McQuaid said.

Mr. Lamontagne said that the governors in the race — Mr. Romney, Mr. Pawlenty, Jon Huntsman Jr. of Utah and perhaps Mr. Perry — can talk about decisions they made in the executive branch.

“You don’t have that benefit as a person in the legislative branch of government,” he said. “So, that’s a little bit of a tough sell to overcome. [Mrs. Bachmann] has to show people what she would do as an executive.”