“What was happening early on was that there was this belief that only those guys had bold ideas,” Ms. Klobuchar, of Minnesota, said in an interview, as she campaigned across New Hampshire this weekend. “I have plans, too. I have bold plans, too. And no one has a monopoly on good ideas.”

As her rivals falter, Ms. Klobuchar has outlasted some national figures, like Senator Kirsten Gillibrand and former Representative Beto O’Rourke, and she is one of just six candidates, so far, to have qualified for the next debate in December. Enough money has flowed in for her to expand her operation; she has doubled her offices in Iowa and her staff in New Hampshire at a time when many of her rivals are worried about contracting. After months stuck toward the bottom of the polls, she has earned around 5 percent in several recent surveys of early-voting states, as voters give her a second look.

And in perhaps the highest mark of progress yet, her strong performance in last week’s debate inspired a spoof on “Saturday Night Live,” albeit one largely focused on her quivering bangs. (Ms. Klobuchar said she was standing under an air vent during the debate and hadn’t used enough hair spray.)

Hoping to ride a wave of post-debate attention, Ms. Klobuchar planned to blaze through New Hampshire, Iowa and South Carolina this week, stopping briefly in Des Moines for a Thanksgiving Day celebration at the home of her campaign’s state chairwoman.

“I’m hearing more talk about Amy. It’s picked up in the last couple weeks,” said Laurie McCray, the Democratic Party chairwoman in Portsmouth, N.H. “People have heard from the other candidates and they’re still looking.”