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CONTOOCOOK, N.H. — Jeb Bush was halfway through an early morning town-hall-style event here Saturday when he paused, announcing he had something he wanted to get off his chest.

“Donald Trump is a jerk,” Mr. Bush said to applause.

“You cannot insult your way to the presidency,” he said. “You can’t disparage women, Hispanics, disabled people. Who is he kidding? This country is far better than that. The idea that he’s actually running for president and insulting people is deeply discouraging, to be honest with you, and I think we should reject that out of hand. I hope you’ll reject it by voting for me, but a guy like that should not be the front-running candidate of our great party.”

Finally finished, Mr. Bush exhaled with a laugh: “I gave myself therapy there.”

Therapy, maybe — but also a deliberate move by Mr. Bush, whose strategy to save his faltering campaign now involves attacking Mr. Trump, forcefully and frequently.

The approach was on display in the Republican debate on Tuesday in Las Vegas, where Mr. Bush repeatedly needled Mr. Trump, seeming to irritate the real estate magnate.

Nonetheless, Mr. Bush still sits in single digits in the polls, and New Hampshire has become a must-win state for him. He must beat, or at the very least tie, his rivals for the party’s more moderate base — Gov. Chris Christie of New Jersey, Gov. John R. Kasich of Ohio and Senator Marco Rubio of Florida — in the primary if he hopes to reinvigorate his campaign.

On Saturday morning, Mr. Bush made an explicit plea to the voters here, asking for their vote and for their active involvement in his campaign.

“I’m going to be up here a lot,” Mr. Bush said. “If I don’t get it today, I’m coming back next week. I’ll ask for it again. And I’m coming back the week after that and the week after that. I love campaigning here and I’m going to ask for your support until I get it.”

Mr. Bush added, almost as if trying to convince himself, “I think you’re looking at the Republican nominee.”

Mr. Bush plans to compete seriously in New Hampshire, with a schedule that has him in the north of the state before Christmas, and back again for several days before New Year’s Day. New Hampshire is the second state to vote, on Feb. 9, eight days after the Iowa caucuses.

On Saturday, Mr. Bush planned a packed schedule of four town-hall-style meetings, intended to show his stamina and resolve. (He has still been unable to shake the “low-energy” stigma Mr. Trump put on him this summer.) A planned fifth event, in Dover, was canceled out of respect for a local Army Ranger who was killed in a training exercise and whose funeral was scheduled for the same time as the Bush event.

At an event in Exeter, N.H., a voter stood and put the question to Mr. Bush: “How can you bring the passion that you’re showing today more broadly to your campaign?”

Mr. Bush said he hoped to appeal to voters in New Hampshire, who will get to see him up close as the “hard-working guy” who is going to “out-campaign people.”

“There’s a mythology built up that somehow I don’t do this every day, I don’t know where it started and I don’t know why it exists,” Mr. Bush said. “Don’t worry about the energy thing. I can outwork everybody running and I’m doing it.”

Later, speaking to reporters, Mr. Bush explained, “You win by making your case in these kinds of settings,” and asked for “a little air” to prove he can energize voters here. Everyone who came up to him after his speech, he said, told him, “I’m in.”

Throughout the day, Mr. Bush fielded questions on issues including college affordability (he said he planned to outline a plan to fix the problem of student loan debt in roughly three weeks) and how to restore America’s position of strength in the world.

But the former Florida governor seemed determined to keep his focus on Mr. Trump, who was busy Friday posting goading Twitter messages aimed at Mr. Bush. And on Saturday, at a rally in Iowa, Mr. Trump again targeted Mr. Bush, calling his campaign “close to incompetent” and noting he was “very close to zero” in the polls.

“He’s an embarrassment,” Mr. Trump said.

Mr. Bush, meanwhile, echoed a line from Tuesday’s debate, repeatedly telling his crowds, “Donald Trump is a chaos candidate, and he would be a chaos president.”

“Did you hear him talk about foreign policy in the debate?” he said in Contoocook. “I mean, it’s like he has no clue.”

At Mr. Bush’s event in Exeter, Jennifer Morrell, 54, said she liked him as her second choice because she thought he would be good on foreign policy and national security. (She said she worried her preferred candidate, Mike Huckabee, does not have a real shot at the nomination.)

But Ms. Morrell also said she had sometimes cringed as she watched Mr. Bush struggle as a candidate.

“I’m kind of embarrassed for him, and I think it’s kind of sad, because I don’t think he’ll get elected, either because there’s just been too many Bushes or because of his performance as a campaigner,” she said as she waited for him to take the stage. “I don’t think he’d be a bad president, but I don’t know if he’s going to get that chance.”

Jeb Bush, Sensing Momentum After Debate, Zeroes In on Donald Trump Mr. Bush’s strategy is risky given how low he has fallen in polls and that several other rivals, like Marco Rubio and Chris Christie, are ahead of him in early voting states.