Although Singer declined to discuss specific conversations with individual politicians, other Republicans have told me that he is close to, and has discussed gay rights with, Gov. Chris Christie of New Jersey, who recently backed off a legal challenge to gay marriage in that state, which became the 14th in which gays and lesbians can legally wed.

I’ve also been told that Singer has had such talks with Senator Rob Portman, the Ohio Republican who came out for gay marriage, citing his love for his gay son. Singer also has a gay son — and a gay son-in-law. The two men are married.

His vision of how Republicans must evolve was echoed in a subsequent conversation that I had with Daniel Loeb, another New York hedge-fund billionaire who has given lavishly to conservatives. Loeb is Singer’s principal financial partner in the H.R.C. international project; Singer has already committed $1.5 million, and Loeb has promised a similar amount over its first years.

When I asked Loeb if opposition to gay rights would increasingly hurt Republicans in elections, he said: “Absolutely. It’s where the country’s gone, and if they don’t go with it, they’ll lose a very important demographic. They already have lost some young people.” Surveys show that more than 70 percent of Americans under 30 favor marriage equality.