WASHINGTON — Dozens of prominent Republicans — including top advisers to former President George W. Bush, four former governors and two members of Congress — have signed a legal brief arguing that gay people have a constitutional right to marry, a position that amounts to a direct challenge to Speaker John A. Boehner and reflects the civil war in the party since the November election.

The document will be submitted this week to the Supreme Court in support of a suit seeking to strike down Proposition 8, a California ballot initiative barring same-sex marriage, and all similar bans. The court will hear back-to-back arguments next month in that case and another pivotal gay rights case that challenges the 1996 federal Defense of Marriage Act.

The Proposition 8 case already has a powerful conservative supporter: Theodore B. Olson, the former solicitor general under Mr. Bush and one of the suit’s two lead lawyers. The amicus, or friend-of-the-court, brief is being filed with Mr. Olson’s blessing. It argues, as he does, that same-sex marriage promotes family values by allowing children of gay couples to grow up in two-parent homes, and that it advances conservative values of “limited government and maximizing individual freedom.”

Legal analysts said the brief had the potential to sway conservative justices as much for the prominent names attached to it as for its legal arguments. The list of signers includes a string of Republican officials and influential thinkers — 75 as of Monday evening — who are not ordinarily associated with gay rights advocacy, including some who are speaking out for the first time and others who have changed their previous positions.

Among them are Meg Whitman, who supported Proposition 8 when she ran for California governor; Representatives Ileana Ros-Lehtinen of Florida and Richard Hanna of New York; Stephen J. Hadley, a Bush national security adviser; Carlos Gutierrez, a commerce secretary to Mr. Bush; James B. Comey, a top Bush Justice Department official; David A. Stockman, President Ronald Reagan’s first budget director; and Deborah Pryce, a former member of the House Republican leadership from Ohio who is retired from Congress.

Ms. Pryce said Monday: “Like a lot of the country, my views have evolved on this from the first day I set foot in Congress. I think it’s just the right thing, and I think it’s on solid legal footing, too.”

Jon M. Huntsman Jr., the former Utah governor, who favored civil unions but opposed same-sex marriage during his 2012 presidential bid, also signed. Last week, Mr. Huntsman announced his new position in an article titled “Marriage Equality Is a Conservative Cause,” a sign that the 2016 Republican presidential candidates could be divided on the issue for the first time.

“The ground on this is obviously changing, but it is changing more rapidly than people think,” said John Feehery, a Republican strategist and former House leadership aide who did not sign the brief. “I think that Republicans in the future are going to be a little bit more careful about focusing on these issues that tend to divide the party.”

Some high-profile Republicans who support same-sex marriage — including Laura Bush, the former first lady; Dick Cheney, the former vice president; and Colin L. Powell, a former secretary of state — were not on the list as of Monday.

But the presence of so many well-known former officials — including Christine Todd Whitman, former governor of New Jersey, and William Weld and Jane Swift, both former governors of Massachusetts — suggests that once Republicans are out of public life they feel freer to speak out against the party’s official platform, which calls for amending the Constitution to define marriage as “the union of one man and one woman.”

By contrast, the brief, shared with The New York Times by its drafters, cites past Supreme Court rulings dear to conservatives, including the Citizens United decision lifting restrictions on campaign financing, and a Washington, D.C., Second Amendment case that overturned a law barring handgun ownership.

“We are trying to say to the court that we are judicial and political conservatives, and it is consistent with our values and philosophy for you to overturn Proposition 8,” said Ken Mehlman, the former chairman of the Republican National Committee, who came out as gay several years ago. He is on the board of the American Foundation for Equal Rights, which brought the California suit, and has spent months in quiet conversations with fellow Republicans to gather signatures for the brief.

In making an expansive argument that same-sex marriage bans are discriminatory, the brief’s signatories are at odds with the House Republican leadership, which has authorized the expenditure of tax dollars to defend the 1996 marriage law. The law defines marriage in the eyes of the federal government as the union of a man and a woman.

Polls show that public attitudes have shifted drastically on same-sex marriage over the past decade. A majority of Americans now favor same-sex marriage, up from roughly one third in 2003.

While Republicans lag behind the general population — the latest New York Times survey found a third of Republicans favor letting gay people marry — that, too, is changing quickly as more young people reach voting age. Several recent polls show that about 70 percent of voters under 30 back same-sex marriage.

“The die is cast on this issue when you look at the percentage of younger voters who support gay marriage,” said Steve Schmidt, who was a senior adviser to the 2008 Republican presidential nominee, Senator John McCain of Arizona, and who signed the brief. “As Dick Cheney said years ago, ‘Freedom means freedom for everybody.’ ”

Still, it is clear that Republican backers of same-sex marriage have yet to bring the rest of the party around to their views. Mr. Feehery said there are regional as well as generational divisions, with opposition especially strong in the South. Speaking of Mr. Boehner, he said, “I doubt very seriously that he is going to change his position.”

Experts say that amicus briefs generally do not change Supreme Court justices’ minds. But on Monday some said that the Republican brief, written by Seth P. Waxman, a former solicitor general in the administration of President Bill Clinton, and Reginald Brown, who served in the Bush White House Counsel’s Office, might be an exception.

Tom Goldstein, publisher of Scotusblog, a Web site that analyzes Supreme Court cases, said the amicus filing “has the potential to break through and make a real difference.”

He added: “The person who is going to decide this case, if it’s going to be close, is going to be a conservative justice who respects traditional marriage but nonetheless is sympathetic to the claims that this is just another form of hatred. If you’re trying to persuade someone like that, you can’t persuade them from the perspective of gay rights advocacy.”