NEW YORK — For years, foes of same-sex marriage had a potent talking point: They’d won every time the issue went to a popular vote. That winning streak has now been shattered in a multi-state electoral sweep by gay marriage supporters — a historic tipping point likely to influence other states and possibly even the Supreme Court.

“It’s an astounding day,” said Kevin Cathcart of the gay-rights group Lambda Legal, recalling that in 2004 alone the gay-marriage movement went 0-13 in statewide elections and was 0-32 overall since 1998.

In Tuesday’s voting, however, Maine and Maryland became the first states ever to approve same-sex marriage by popular vote. Washington state seemed poised to follow suit, although slow ballot-counting there continued Wednesday. And in Minnesota, voters rejected a proposal to place a ban on gay-marriage in the state constitution, a step taken in past elections in 30 other states.

“The anti-gay opposition kept moving the goal posts and had as their last talking point that we could not win a popular vote,” said Evan Wolfson, president of the advocacy group Freedom to Marry. “Last night, voters in Maine, Maryland, Minnesota, and, all signs suggest, Washington proved them wrong, wrong, wrong and wrong.”

Heading into the election, gay marriage was legal in six states and the District of Columbia, in each case due to legislation or court orders rather than popular vote.

Activists said Tuesday’s results will likely spur pushes for same-sex marriage in states that already have established civil unions for gay couples — including Illinois, Rhode Island, Hawaii and Delaware.

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Democratic takeovers of both legislative chambers in Colorado and Minnesota may also prompt moves there to extend legal recognition to same-sex couples. In each state, the Democratic governors, John Hickenlooper of Colorado and Mark Dayton of Minnesota, would support such efforts.

In Minnesota, state Sen. Scott Dibble, who is openly gay, is among several Democratic lawmakers uncertain if an immediate push for gay marriage makes political sense. But Dibble, who is 47, said of himself and his partner: “We’ll be married in Minnesota in our lifetime.”

Whatever happens at the statehouse level, the U.S. Supreme Court is also likely to become a pivotal battleground in the next phase of the gay-marriage debate.

The justices are expected to confront same-sex marriage in some form during the current term.

Several pending cases challenge a provision of the 1996 Defense of Marriage Act that deprives same-sex couples of federal benefits available to heterosexual couples. A separate appeal asks the justices to decide whether federal courts were correct in striking down California’s Proposition 8, the amendment that outlawed gay marriage after it had been approved by courts in the nation’s largest state.

“The justices now know America is with us. America is ready,” said Brian Ellner, co-founder of a social-media initiative called TheFour.com that was active in the gay-marriage campaigns. He and other activists noted that nationwide polls prior to the election were showing, for the first time, that a majority of Americans now backed gay marriage.

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James Esseks, director of the American Civil Liberties Union’s Lesbian Gay Bisexual and Transgender Project, termed the referendum results “an indisputable watershed moment” that almost certainly would influence the Supreme Court.

“When making decisions on civil rights issues, the court follows the country, rather than leading,” he said. “They don’t make decisions in a complete public-opinion vacuum.”

He noted that if the high court struck down Prop 8, that would immediately add California — with its 37 million residents — to the list of states allowing same-sex marriage.

Had the four measures lost, said Evan Wolfson, justices might have been reluctant to wade in on the side of gay marriage. Now, he said, they could do so “knowing that their support will stand the test of time and, indeed, be true to where the American people already are.”

The chairman of the leading advocacy group opposing same-sex marriage, John Eastman of the National Organization for Marriage, said it was possible that the referendum results might nudge the high court toward a ruling favoring gay marriage. But Eastman said it also was possible the justices would decide to let the political process play out a bit longer at the state level before intervening.

The National Organization for Marriage’s president, Brian Brown, expressed disappointment at the unprecedented losses for gay marriage opponents, who were outspent by at least 3-to-1 in the four referendum states — all of them won easily by President Barack Obama..

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The results “reflect the political and funding advantages our opponents enjoyed in these very liberal states,” Brown said. “Our opponents and some in the media will attempt to portray the election results as a changing point in how Americans view gay marriage, but that is not the case.”

For the gay-rights movement, the celebration extended far beyond the groundbreaking ballot measures.

In Wisconsin, veteran congresswoman Tammy Baldwin became the first openly gay person elected to the U.S. Senate. At least five other openly gay Democrats were elected to House seats, while Kyrsten Sinema — vying to be the first openly bisexual member of Congress — was locked in a too-close-to-call race in Arizona.

In Iowa, gay-marriage opponents failed on two counts. They lost a bid to oust one of the state Supreme Court justices who ruled in favor of gay marriage in 2009, and they were unable to take control of the state Senate, where Democratic Majority Leader Michael Gronstal has blocked a proposed amendment to overturn that ruling.

More broadly, gay-rights leaders celebrated the re-election of Obama, who had frustrated them early in his term with his sometimes cautious stances. Over the past two years, he’s become a hero of the movement — playing a key role last year in enabling gays to serve openly in the military and this year becoming the first sitting president to endorse same sex-marriage.

Among the next agenda items at the federal level is the proposed Employment Nondiscrimination Act, which would protect gays and transgender people from workplace discrimination.

The gay-rights momentum even extended overseas. Spain’s top court upheld the legality of the country’s gay marriage law on Tuesday, and French President Francois Hollande’s Cabinet was pushing ahead Wednesday with a controversial bill that could see gay marriage legalized early next year.