GREEN BAY, Wis. — A bastion of “Midwestern nice.” An opening for Senator Ted Cruz. Swelling doubts about the go-it-alone approach of Donald J. Trump.

Since his loss in Iowa, Mr. Trump has wanted a rematch with Mr. Cruz. In Wisconsin — another state stocked with conservative activists desperate to stop Mr. Trump — he is getting something like it. And it is not going so well.

As the state prepares to vote on Tuesday, the candidates are at it again, circling and prodding each other in a final sprint before the high-profile contest, which could have outsize ramifications for the Republican nominating contest as Mr. Trump struggles to avoid a contested convention.

And for both campaigns, these final Wisconsin days are proving to be both a necessary stress test and, depending on the results, a likely bellwether of candidate strategy for the rest of the primary season.

Mr. Cruz, who leads Mr. Trump by about 10 percentage points here, according to recent polls, is field-testing a new playbook: exploiting Mr. Trump’s growing unpopularity with women — a gambit that crested last week with the introduction of a Women for Cruz coalition, headlined by Mr. Cruz’s wife and mother.

And Mr. Trump, who tends to eschew the backslapping, handshaking retail politics of traditional campaigns in favor of large rallies, finds himself in a situation he has not faced since the Iowa caucuses: behind in the polls, not entirely in control and forced to focus, laserlike, on just one crucial state.

After something of a spring break from the trail after the Florida primary, where he dispatched Senator Marco Rubio in his home state, Mr. Trump returned to Wisconsin a week before its primary, with a rally in House Speaker Paul D. Ryan’s hometown. And — for Mr. Trump, at least — he has maintained a breakneck schedule, with three events throughout the state on Saturday and another three planned for Monday.

Mr. Trump, who prefers to return to Manhattan after evening events to sleep in his own bed, even spent the night in a downtown Milwaukee hotel, staying locally overnight just as he did at the end of the Iowa contest.

On Sunday, Mr. Trump missed the bris for his new grandson, Theodore James Kushner, to stop by Miss Katie’s Diner in Milwaukee, where he walked in and waved before posing for pictures with about a third of the patrons. Retail politics swiftly checked off, he sat down with six of his staff members for breakfast (fried eggs, bacon and hot chocolate with whipped cream) and had a 20-minute chat with reporters.

Despite the headwinds in Wisconsin, where conservatives like Gov. Scott Walker have aligned against him en masse, Mr. Trump rejected comparisons to Iowa, where he finished behind Mr. Cruz before going on to win the New Hampshire primary in his first victory of the cycle.

Wisconsin, he told reporters, “feels very much like New Hampshire to me.”

“Trump wasn’t going to win New Hampshire, and then all of a sudden, we win in a landslide,” he said. “Because I could I feel it with the people. I can feel it with the people in Wisconsin.”

The scramble comes as Mr. Cruz is working hard to outmaneuver Mr. Trump in the shadow primary for convention delegates, leaning on a cadre of campaign officials and loyal activists well versed in the arcana of party rules.

And in the primaries themselves, Mr. Cruz’s ground game, which helped lift him to victory in Iowa, has followed him to Wisconsin, where another “Camp Cruz” has been set up for out-of-state volunteers. One of them, Sam Kinnaman of St. Louis, said he had now worked for Mr. Cruz in five states.

At a campaign office on Saturday in Waukesha, a man in a cowboy hat and another in a Green Bay Packers Cheesehead stood shoulder to shoulder as supporters placed calls to Wisconsin voters. The highest-energy Cruz volunteers appeared to be the senator’s own daughters, ages 7 and 5, who paid a visit to the office with their mother, Heidi, and held a competition: Who could greet the most voters?

“Hi, my name is Caroline. Thanks for supporting my dad,” the older daughter told strangers on a loop. “I’ll be 8 in 12 days.”

At a rally here on Sunday, Mr. Cruz reveled in the presence of some recent supporters: Mr. Walker, Senator Mike Lee of Utah, Carly Fiorina and Kabeer Gbaja-Biamila, a former star defensive player for the Packers.

Addressing the crowd in a hotel ballroom, Mr. Cruz imagined aloud the prospect of Mr. Gbaja-Biamila’s chasing Mr. Trump on a football field. “I think Donald’s hair would stand on end,” he said.

Mr. Trump’s support on the ground has been harder to trace, and the primary offers a critical test for a campaign that has often struggled with its organization, in Iowa and beyond. (Mr. Trump has maintained that Mr. Cruz “stole” Iowa with caucus-night shenanigans; his crowds are now conditioned to chant “Lyin’ Ted” — Mr. Trump’s favored nickname for his rival — when his name is invoked at rallies.)

The contest also follows a series of missteps and misstatements Mr. Trump has made in recent weeks, which could hurt him both in the coming Republican nominating contests and in a general election, especially among female voters.

He first drew criticism after reposting an unflattering photo of Mr. Cruz’s wife juxtaposed with his wife, Melania, a former model, though he later told Maureen Dowd, a New York Times columnist, that had been “a mistake.” More recently, he stumbled through a series of interviews on the topic of abortion, first saying that women who have illegal abortions should face some form of “punishment,” then recalibrating.

In recent days, he has dispatched Sarah Palin, the former Alaska governor, in hopes of bolstering his credibility with conservatives. But speaking at a local party dinner on Friday in Milwaukee, where Mr. Cruz and Gov. John Kasich of Ohio also held forth, Ms. Palin struggled to connect.

She drew only occasional applause in a disjointed, uncomfortable speech, and several attendees giggled as she spoke. Some former admirers of Ms. Palin said they could not reconcile her support for Mr. Trump.

“I don’t want to be afraid to vote for a candidate,” Suzanne Frohna, 65, of Cudahy, said of Mr. Trump, before appraising Ms. Palin’s speech as “tweety, like a bird.” “I wouldn’t be afraid to vote for Cruz,” she added.

At the diner on Sunday, where Mr. Trump stopped in, the reception was mixed. Some customers shook his hand and posed for pictures, offering menu suggestions. (One suggested the three-cheese omelet, another the steak and eggs.) But others were less enthusiastic.

As the candidate left, a man eating breakfast turned to a photographer with a question: “Did anyone take a picture of the deafening silence?”