WASHINGTON — Hillary Rodham Clinton’s embrace of gay marriage Monday signals she may be seriously weighing a 2016 presidential run and trying to avoid the type of late-to-the-party caution that hurt her first bid.

Her chief Democratic rivals endorsed same-sex marriage as much as seven years ago, and it’s widely popular with Democratic and independent voters.

By supporting gay marriage a full two years before the next presidential primary warms up, Clinton may render the issue largely settled among Democrats, should she decide to run.

But things could be vastly different in the November 2016 general election, regardless who wins the Democratic nomination. That nominee is virtually certain to support same-sex marriage, whereas there’s a strong possibility the Republican nominee will not.

That could be a problem for the GOP nominee if same-sex marriage becomes a prominent issue. A poll released Monday shows a dramatic shift in attitudes about legalizing gay marriage, with 58 percent of Americans now supporting it.

Three years ago, the figure was 47 percent, the ABC News/Washington Post poll reported.

Partisan breakdowns show why it’s virtually essential for a Democratic presidential hopeful to support same-sex marriage, and why it’s difficult for GOP contenders to do the same.

Seventy-two percent of Democrats, 62 percent of independents and 34 percent of Republicans support same-sex marriage, the ABC-Post poll found. Unless Republicans’ opinions change significantly in the next two years, a GOP presidential hopeful may struggle to win the nomination without opposing gay marriage, even if the position causes problems in the November general election.

For those who lived “through the long years of the civil rights and women’s rights movements, the speed with which more and more people have come to embrace the dignity and equality of LGBT Americans has been breathtaking and inspiring,” Clinton said in a six-minute video, referring to lesbian, gay, bisexual and transgender persons.

In the video, released by the gay rights advocacy group Human Rights Campaign, Clinton says gays and lesbians are “full and equal citizens and deserve the rights of citizenship.”

“That includes marriage,” she says, adding that she backs gay marriage both “personally and as a matter of policy and law.”

Clinton recently stepped down as secretary of state, freeing her to talk more openly about U.S. domestic political matters. Some Democratic activists cautioned that her Monday statement isn’t a sure sign she plans to run for the office that her husband, Bill, won two decades ago.