In recent years, he has frequently deployed his network to cultivate up-and-coming Republicans who he believes can help expand the party’s demographic appeal. Among them are Representative Elise Stefanik of New York, the youngest woman ever elected to Congress, and Mr. Rubio himself, whom Mr. Singer backed early in his 2010 race when many of Mr. Singer’s peers sided with Charlie Crist, then Florida’s Republican governor — a moment that was seen as a turning point in the race.

The battle for Mr. Singer’s support — which included months of behind-the-scenes lobbying by aides and appearances by candidates over the last year at dinners and breakfasts convened by Mr. Singer — underscores the growing clout of big donors in presidential elections, particularly this year, when “super PACs,” and the wealthy donors who finance them, have moved to the center of the race.

But Mr. Singer provides something that some other coveted Republican donors do not. Unlike Sheldon Adelson, a fellow Republican billionaire and Israel supporter, Mr. Singer is an assiduous and effective “bundler” for candidates: In the 2012 campaign, he raised more than $3 million to try to help elect Mitt Romney, the eventual Republican nominee. Many other donors, particular in the New York financial world, turn to Mr. Singer’s political advisers for strategic guidance on their own donations.

And Mr. Rubio, who struggled to raise campaign cash over the summer and has relied heavily on outside groups to pay for advertisements promoting him, needs their help.

Both Mr. Rubio and Mr. Bush eagerly sought Mr. Singer’s backing, as did Mr. Christie, and all three have ties to the wealthy hedge fund manager.

Mr. Rubio has aggressively embraced the cause of wealthy pro-Israel donors like Mr. Adelson, whom the senator is said to call frequently, and Mr. Singer, who both serve on the board of the Republican Jewish Coalition, an umbrella group for Republican Jewish donors and officials. Mr. Bush has been less attentive, in the view of some of these donors: Last spring, he refused to freeze out his longtime family friend James A. Baker III, the former secretary of state, after Mr. Baker spoke at the conference of a liberal Jewish group.