For Mr. Cruz, help from establishment donors could dilute his outsider message and provide a new cudgel for Mr. Trump, who has denounced rivals for their dependence on contributions from the wealthy and powerful.

But as Mr. Cruz prepares for a long march to the Republican convention in July in Cleveland, he would not mind those donors’ help: His campaign, long powered by a loyal cadre of small contributors, spent far more money than it raised in January and February — burning through about $10 million more than it took in. (At his Wisconsin victory speech, Mr. Cruz said that the campaign had raised more than $2 million on Tuesday alone.)

Forty percent of his overall cash has come from small donors, many in Texas, and only about a fifth of his money for the primary has come from donors giving the maximum $2,700 contributions. At the end of February, according to the most recent financial disclosures, the campaign reported about $8 million cash on hand.

Mr. Cruz’s challenge is to broaden his reach in the world of midlevel Republican fund-raisers — those who can raise tens or hundreds of thousands of dollars for his campaign — and among the elite group of billionaires who could write larger checks to the super PACs supporting him.

But doubts remain. Mr. Catsimatidis, one of about 30 people who attended the event at the Knickerbocker Club, pronounced Mr. Cruz “very, very smart,” but he said he wondered why “out of 100 people in the Senate, 99 don’t like him.”

Mr. Cruz is not always good at asking for help, sometimes giving the impression that he could as easily do without it. Even in private, donors said, he can be prone to sanctimony, disinclined to adjust his television-ready populism. Allies view Mr. Cruz’s uncompromising style as a virtue, but they concede it can make life difficult on the donor circuit.