In the end, at least one senator from each of the states polled voted for the bill.
Susan Collins of Maine, who was the lead Republican negotiator in the Senate, credited Mr. Mehlman and the outside group’s efforts with helping to get her party over the finish line.
“It all helped shore up our supporters, and it certainly helped get us over the magic number of 10,” Ms. Collins said in an interview. “It made our supporters feel less alone, but it also played a critical role in getting us the margin. It gave Republicans who were on the bubble a sense of comfort.”
Mr. Mehlman, who has worked to build greater acceptance among Republicans for gay- and transgender-friendly policies, also leaned on a network of Republicans that he enlisted in 2019 to urge the Supreme Court to declare that the Civil Rights Act of 1964 explicitly prohibits discrimination against gay men, lesbians and transgender people in the workplace.
“We have a network of individuals who live in these states, are active in these states, who also believe in the freedom to marry,” Mr. Mehlman said. “They were pleased to make their case to the senators directly, or through op-eds.”
Proponents also made personal appeals for the legislation, with arguments tailored to a conservative audience. Back in July, after it passed the House, Mr. Mehlman and Theodore Olson, a former solicitor general, published an op-ed in The Wall Street Journal urging the Senate to follow suit and asserting that “as conservatives we should promote freedom and limited government. That includes supporting American citizens’ freedom to marry the person they love.”
The group took out a full-page advertisement in The Journal in September, publishing a letter signed by 450 prominent Republicans supporting the legislation, including Olympia Snowe, the former Republican senator from Maine; Tony Fabrizio, the G.O.P. pollster who worked for former President Donald J. Trump; Ben Ginsberg, the prominent Republican lawyer; Mary Cheney, the openly gay and married daughter of former Vice President Dick Cheney; Tom Ridge, the former homeland security secretary under Mr. Bush; and Governor Charlie Baker of Massachusetts.
Ms. Collins said the effort was critical, especially because of the pressure some Republicans were under to oppose the bill.
