New York ? Many obstacles still lie ahead for supporters of same-sex marriage, and eventually they will need Congress or the Supreme Court to embrace their goal. For the moment, though, they are jubilantly channeling the lyrics of “New York, New York.”

“Now that we’ve made it here, we’ll make it everywhere,” said prominent activist Evan Wolfson, who took up the cause of marriage equality as a law student three decades ago.

With a historic vote by its Legislature late Friday, New York became the sixth — and by far the most populous — state to legalize same-sex marriage since Massachusetts led the way, under court order, in 2004.

With the new law, which takes effect after 30 days, the number of Americans in same-sex marriage states more than doubles. New York’s population of 19 million surpasses the combined total of Massachusetts, Connecticut, Vermont, New Hampshire and Iowa, plus the District of Columbia.

The outcome — a product of intensive lobbying by Democratic Gov. Andrew Cuomo — will have nationwide repercussions. Activists hope the New York vote will help convince judges and politicians across the country, including a hesitant President Barack Obama, that support of same-sex marriage is now a mainstream viewpoint and a winning political stance.

“New York sends the message that marriage equality across the country is a question of ‘when,’ not ‘if,”‘ said Fred Sainz, a vice president of the Human Rights Campaign.

Wolfson, president of the advocacy group Freedom to Marry, said the goal is attainable by 2020, or sooner, “if we do the work and keep making the case.”

The work — as envisioned by leading activists — is a three-pronged strategy unfolding at the state level, in dealings with Congress and the Obama administration, and in the courts where several challenges to the federal ban on gay marriage are pending.

“This will be a big boost to our efforts nationally,” said Richard Socarides, a former Clinton White House adviser on gay rights. “It will help in the pending court cases to show that more states are adopting same-sex marriage, and it will help in the court of public opinion.”

The New York bill cleared the Republican-controlled Senate by a 33-29 margin, thanks to crucial support from four GOP senators who joined all but one Democrat in voting yes. The Democratic-led Assembly, which previously approved the bill, passed the Senate’s stronger religious exemptions in the measure, and Cuomo swiftly signed it into law.

Gay rights activists have been heaping praise on Cuomo for leading the push for the bill, seizing on an issue that many politicians of both parties have skirted. Yet the Senate vote marked the first time a Republican-controlled legislative chamber in any state has supported same-sex marriage, and several prominent Republican donors contributed to the lobbying campaign on behalf of the bill.

For those engaged in the marriage debate nationally, recent months have been a political rollercoaster.

Bills to legalize same-sex marriage failed in Maryland and Rhode Island despite gay rights activists’ high hopes. However, Illinois, Hawaii and Delaware approved civil unions, joining five other states — California, Nevada, New Jersey, Oregon and Washington — that provide gay couples with extensive marriage-like rights.

Adding those eight states to the six that allow gay marriage, more than 35 percent of Americans now live in states where gay couples can effectively attain the rights and responsibilities of marriage. Just 11 years ago, no states offered such rights.

For now, gay couples cannot get married in 44 states, and 30 of them have taken the extra step of passing constitutional amendments banning gay marriage. Minnesota’s Republican-controlled Legislature has placed such an amendment on the 2012 ballot.

Brian Brown, president of the conservative National Organization for Marriage, vowed to seek defeat of the New York Republicans who helped the marriage bill pass. He also predicted victory for the amendment to ban gay marriage next year in Minnesota, and said this would belie the claims that the same-sex marriage campaign would inevitably prevail nationwide.

“We’ve won every free, fair vote of the people,” Brown said Saturday. “Backroom deals in Albany are not an indication of what people in this country think about marriage.”

Several recent opinion polls — by Gallup and The Associated Press, among others — have shown that a majority of Americans now approve of same-sex marriage, which a decade ago lagged below 40 percent support. Particularly strong backing for gay marriage among young people, who’ve grown up watching gay friendly films and TV programs, has prompted many analysts across the political spectrum to suggest the trend is irreversible.