MADISON, Wis. — Senator Ted Cruz of Texas, eyeing a victory here that could reshape the race for the Republican presidential nomination, has appeared most vexed by a rival he views as more of a long-term nuisance than a short-term threat: Gov. John Kasich of Ohio.

As Mr. Cruz looks beyond Wisconsin, where he is favored to defeat Donald J. Trump on Tuesday, his frustrations with Mr. Kasich have increasingly been laid bare. With activists and operatives opposed to Mr. Trump fanning out across the electoral map in a scramble to deny him the nomination, Mr. Cruz’s team has argued that it is Mr. Kasich’s “quixotic” bid for the White House that will prove the biggest boon to Mr. Trump in the states to come.

On Monday, Mr. Cruz amplified calls for Mr. Kasich to step aside and predicted that “the people would quite rightly revolt” if party leaders tried to elevate anyone other than Mr. Cruz or Mr. Trump at a contested convention in July.

Mr. Cruz has begun airing ads in Wisconsin accusing Mr. Kasich of cronyism as Ohio’s governor. He has sent mailers attacking Mr. Kasich’s record on spending and his views on the Second Amendment. And his team has accused Mr. Kasich of auditioning to be Mr. Trump’s vice president, with some joking that he must be receiving some sort of payment.