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?