The American Academy of Pediatrics says that a child's health benefits from a stable relationship between parents, no matter their sexual orientation. A new poll finds 49 percent of Americans favor same-sex marriage.

Politicians, business leaders, athletes and other high-profile figures are racing to announce their support for gay marriage before the Supreme Court holds landmark arguments next week — an unusually broad and public push.

Many of them have filed formal briefs with the court. Others have stayed out of the legal case but made public declarations that they said were carefully timed in hopes that they might sway the justices.

“Those kinds of things make the court feel that what they’re doing is sensible,” said Alan Morrison, who teaches constitutional law at George Washington University. “It may not affect the constitutional questions, but the court does want to feel comfortable.”

On Thursday, the American Academy of Pediatrics, which represents 60,000 doctors, published a policy statement saying that whether a child is raised by gay or straight parents has no effect on development.

Dr. Thomas McInerny, president of the academy, told NBC News that the policy change was in the works for two years but that the academy hurried its announcement so the policy would be available for the justices.

“We are an apolitical organization,” he said. “On the other hand, we do feel very strongly about the best interests of children.”

The court will hear arguments in two cases. One is about Proposition 8, a ban on gay marriage approved by California voters in 2008. The other is about the 1996 Defense of Marriage Act, which blocked federal recognition of same-sex unions.

In the final days before a Supreme Court deadline to file papers in both cases, prominent Republicans rushed to add their names to a brief arguing that gay marriage promotes the conservative values of stability and mutual obligation.

Besides former governors and members of Congress, the 131 signers of the brief included top aides in the administration of George W. Bush and senior advisers to the presidential campaigns of Sen. John McCain in 2008 and Mitt Romney last year.

And last week, Sen. Rob Portman of Ohio became the first Republican senator to support same-sex marriage. Portman, whom Romney considered as a running mate, said that he had had a change of heart on the matter after his son, who is 21, came out.

Portman did not sign the Republican brief before the Supreme Court but said that the upcoming arguments were a factor in his decision to go public.

Hillary Rodham Clinton, the former secretary of state and a potential Democratic presidential candidate in 2016, released a video last week through a gay rights group and said flatly: “I support marriage for lesbian and gay couples.” As a candidate in 2008, she had opposed gay marriage but supported civil unions.

Her announcement came after her husband, who signed the Defense of Marriage Act into law as president, published an Op-Ed in The Washington Post encouraging the Supreme Court to overturn it.

“I now know that, even worse than providing an excuse for discrimination, the law itself is discriminatory,” he wrote.

Morrison, from George Washington University, who filed a brief that called parts of DOMA “utterly irrational,” said that the gay rights cases may be unprecedented in drawing support from such a broad spectrum of society.

Earlier this month, more than 100 corporations, including Google, Nike and Estee Lauder, signed two briefs in support of gay marriage — arguing that blocking recognition is just not legally wrong but hurts their businesses.

Lloyd Blankfein, the head of the investment bank Goldman Sachs, told The New York Times that captains of industry “wanted to attach themselves to what may be the last great civil rights issue of our time.”

And on Monday, Rashad Evans, a mixed martial arts fighter, told the gay website Outsports that he felt a duty to support gay rights as a competitor in “a macho-type sport.”

“I have kids,” he told the site. “I don’t want them growing up in a society where they, or their friends, could be second-class citizens based on which person they fall in love with or who they want to be happy with.”

He joined a brief filed by Chris Kluwe, a punter for the Minnesota Vikings, and Brendon Ayanbadejo, a linebacker for the Baltimore Ravens.

Marc Solomon, national campaign director for the gay rights group Freedom to Marry, said that his group was pleased that the cause had drawn such broad support, particularly from the political right.

“Our side has put forth the most powerful case that could be made that America is ready,” he said. “There is no question that justices live in the real world.”

Polls show increasing public support for gay marriage. A Washington Post-ABC survey earlier this week found 58 percent for gay marriage and 36 percent opposed — a mirror image of public opinion less than a decade ago.

Brian Brown, president of the National Organization for Marriage, a leading group opposed to same-sex marriage, said that the pediatrics academy had taken a “transparently political step” by endorsing gay marriage and had been influenced by studies produced by gay-marriage advocates.

“Which parent can a child do without — her mother or her father?” he said in a statement. “We remain confident that the U.S. Supreme Court will uphold the ability of states and the federal government to define marriage as the union of a man and a woman, a definition that has served our nation well for hundreds of years.”

Another group opposed to gay marriage, the Traditional Values Coalition, mocked Portman’s announcement last week by publishing a hypothetical statement from a parent who came out in favor of drunken driving because her son is a drunk driver.

When the Supreme Court takes up the question Tuesday and Wednesday, most of the public statements won’t matter, said Tom Goldstein, a founder of the widely read Scotusblog, which analyzes the court.

What’s more, he said, “Some of these developments are a double-edged sword. The cases rely to some extent on the notion that homosexuals face widespread discrimination and hostility. The fact that the country is coming around so fast ironically could hurt their cause in court.”

The announcement by the pediatrics academy could matter because it speaks directly to conservatives and their concerns in the case, he said, but “what someone thinks in Hollywood couldn’t be more irrelevant.”

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