For gay-rights advocates, if there was any conceivable downside to their definitive victory  at the Supreme Court last month, it was the sense of finality that came with it. There was no equivocation, no qualifiers, no hedging in the Court’s decision. The right for same-sex couples to marry is now enshrined in the Constitution, culminating a decades-long battle that accelerated rapidly to a decisive victory in the last few years. They had won.

With their most important goal achieved, what more could they want? Quite a lot, it turns out.

“Despite how far we’ve come, we cannot mistake our progress for victory,” said Winnie Stachelberg, the executive vice president for the Center for American Progress, the liberal think tank.

On Thursday, Democrats in Congress gathered with activists at the Capitol to introduce sweeping legislation that would protect LGBT Americans from discrimination on the basis of sexual orientation or gender identity. The proposal is remarkable in its scope: Where Democrats had previously tried and failed to pass legislation banning discrimination only in employment—the Employment Non-Discrimination Act, or ENDA—the party is now rallying behind a proposal that would extend those protections in education, housing, public accommodations, and any other area of law where discrimination has been prohibited for other protected classes.

Democrats are clearly trying to seize on the momentum from the Supreme Court decision, despite the fact that the legislation faces especially long odds in the Republican-controlled Congress. “This is going to be the heaviest lift in the history of our movement,” Chad Griffin, president of the Human Rights Campaign, told The Washington Post. In 2013, the Senate passed the more narrowly-written Employment Non-Discrimination Act with some help from Republicans, but it never got a vote in the House under Speaker John Boehner, who said at the time it was “unnecessary” and would provoke “frivolous lawsuits.”

Representative David Cicilline of Rhode Island, the chief sponsor of the new Equality Act, said he had already been asked why he would push for such an ambitious proposal when ENDA had failed for years. “The answer is that our country is in a different place today, and momentum is on our side,” he said on Thursday. “Partial equality is not acceptable. It’s time for a comprehensive bill that protects LGBT Americans from discrimination in all aspects of everyday life.”

Thirty-one states lack such protections for LGBT people, according to the lawmakers and advocates, and they criticized what they called a patchwork of laws that required a federal solution. “An LGBT person could get married on Saturday, post photos of their wedding on Sunday, and get fired from their job or thrown out of their apartment on Monday,” Cicilline said, repeating a version of a talking point that’s become popular in the weeks since the Supreme Court ruling was handed down. (In Griffin's version, all four of those things can happen in the same day.) A ruling last week by the Equal Employment Opportunity Commission might offer some more protections for federal workers, but as my colleague Joe Pinsker writes, its impact on the private sector is less clear.

The Equality Act has already amassed broad support within the Democratic Party; more than 80 percent of Democrats in the House and 40 out of 45 senators had signed on by the time it was introduced, and Hillary Clinton quickly endorsed it with a tweet. Yet its path to passage is all-the-more arduous because conservatives in Congress are pushing a much different response to the marriage ruling: additional religious-liberty protections for businesses or groups that oppose same-sex marriage.

Already, more than half of the Republican House conference has endorsed the First Amendment Defense Act (a moniker just as difficult to oppose as the Equality Act), which bars the federal government from taking “any discriminatory action” against people or groups “with a religious belief or moral conviction that marriage is or should be recognized as the union of one man and one woman, or that sexual relations are properly reserved to such a marriage.” That would include, for example, denying tax-exempt status to churches or religious groups, or withholding other federal benefits. Whether that bill goes anywhere is also uncertain. Congressional aides doubt it has the support to pass, and critics have suggested that the bill's language on “sexual relations” is so broad that it could allow employers to fire an unmarried woman for getting pregnant. The party leadership is under heavy pressure to bring it to a vote, but senior Republicans likely are wary of risking the political firestorm that engulfed Indiana Governor Mike Pence (himself a former congressional leader) when he signed the Religious Freedom Restoration Act earlier this year.

The more politically-savvy move that Republicans could make is one that Representative Charlie Dent, a more centrist member from Pennsylvania, floated to his colleagues last week. Dent’s still-in-the-works proposal would combine a more limited religious-freedom bill with expanded LGBT non-discrimination protections for employment and housing. “This opens up a can of worms, and Congress needs to show it can do two things at once: protect religious freedoms and provide legal protections for nondiscrimination,” Dent told The New York Times. Splitting the difference might be too much for the House’s hardline conservatives, and gay-rights advocates might have little reason to compromise after winning such a decisive marriage victory in court, particularly heading into the 2016 presidential campaign.

As Nancy Pelosi, the House Democratic leader, noted on Thursday, extending anti-discrimination protections to the LGBT community is the last of four major priorities the gay-rights movement was pursuing when Obama took office. In 2009, Congress expanded the hate-crimes law to including sexual orientation. In 2010, the ban on gays serving openly in the military was lifted, and last month same-sex marriage became legal across the country. It might only be a matter of time before that final hurdle is cleared, but that doesn’t mean it’ll happen soon.