On Thursday, Sen. Jeff Merkley and Rep. David Cicilline are set to propose historically broad non-discrimination bills that will protect Americans from losing their jobs—or from being evicted from their apartment or other forms of discrimination—because of their sexual orientation or gender identity. Supporters of the bills are using the fact that marriage is newly legal in all 50 states as both a springboard and justification for this next battle to win civil rights for the LGBT community.

The Equality Act will cover the areas of employment, education, housing, public accommodations, jury service, federal funding and credit. “You can be married on Saturday, post your wedding pictures on Facebook on Sunday and be fired from your job or kicked out of your apartment on Monday,” says Cicilline, who became the fourth openly gay member of Congress in 2010. The legality of same-sex marriage, he says, “creates a sense of urgency,” because it will lead to LGBT people living more openly but consequently expose them to the possibility of more discrimination.

There is a vast misconception that it is already illegal to discriminate against gay people—one poll put the number at 87% who believe so—but there are no federal laws that set out protections for LGBT Americans. Twenty-one states currently prohibit discrimination based on sexual orientation, and 18 of those, as well as the District of Columbia, also include gender identity. “There is a huge hurdle our community needs to overcome to convince people that this kind of discrimination is—A—perfectly legal, and—B—actually exists,” says Winnie Stachelberg from the Center for American Progress.

In December, that progressive think tank put out a report to refute the notion that protections for LGBT Americans are “unnecessary,” as conservatives such as House Speaker John Boehner have argued. One in ten lesbian, gay or bisexual people say they’ve been fired from a job because of their sexual orientation, they reported, while nearly one in three transgender people reports being treated unequally at a retail store.

A lesbian couple in Michigan, where a GOP lawmaker tried but failed to pass a non-discrimination law last year, says a pediatrician recently refused to see their six-day-old baby after she “prayed” on the matter. There was no statute under which the couple could file a complaint, says report author Sarah McBride. But, she adds, non-discrimination laws aren’t just about recourse. “They’re also about preventing bad behavior,” she says. “They’re also about making clear what our values are as a country and what we expect our citizens to do, and that’s to treat everyone fairly and with respect.”

A bill that would make it illegal to discriminate against LGBT people when it comes to hiring and firing has been introduced in some form—and then failed to become law—in nearly every Congress for the past two decades. But rather than have another go at passing the Employment Non-Discrimination Act, or even a broader bill that creates a new law, Merkley and Cicilline are trying a different strategy: amending existing statutes like the Civil Rights and Fair Housing acts so that those long-established protections are extended to cover sexual orientation and gender identity, in addition to race, sex, religion or national origin.

“The only way that we can achieve full equality for the LGBT community,” says Cicilline, “is to make them part of this well-accepted civil rights construct.”

The move is designed, in part, to make it harder to object to the bill—because the Equality Act will “literally be extending the exact same protections” other classes already have—and to stymie the inevitable objections about religious freedom, which almost always crop up alongside debates over such non-discrimination bills.

“It has the value of saying, Look, whatever religious exemptions currently exist in these other protected categories—race, religion, gender, ethnic origin—those same religious exemptions would exist in the context of the LGBT community,” Cicilline says. “Not a single person’s right to exercise their religious tradition or to honor the practices of their own religion are compromised by this legislation.”

Critics of such bills say that legally obliging, say, a pizzeria to cater a same-sex wedding, violates a person’s right to oppose such unions based on religious or moral beliefs. With the battle over same-sex marriage lost, many conservatives are turning their efforts to pushing “religious freedom” or “First Amendment defense” bills to give people legal arguments for such refusals. A poll released earlier this month found that a small majority of small business owners—55%—believe businesses should not be allowed to deny wedding-related services to a same-sex couple based on religious beliefs.

Republicans Sen. Mike Lee and Rep. Raul Labrador introduced companion bills in June aimed at “protecting religious freedom from Government intrusion,” stating that “conflicts between same-sex marriage and religious liberty are real.” While they say their bill is aimed at making sure organizations like religious schools can’t lose their tax-exempt status for opposing same-sex marriage, progressives say it threatens to “undermine” protections Obama extended to millions of LGBT workers with an executive order, as well as the future of a broad non-discrimination law.

Merkley announced in December that a big proposal was coming. The scores of lawmakers he and Cicilline expect to co-sponsor the bills are rehashing this old fight in a time when there are new levels of awareness and acceptance for LGBT Americans, particularly among young people. According to Gallup, a record high 60% of Americans now support same-sex marriage, up from 50% in 2012 and 40% in 2009. Once people learn that protections for LGBT people don’t exist federally or in many states, “they overwhelmingly support the basic idea that LGBT Americans should be judged only on their merits, just like everyone else,” Merkley tells TIME. “It’s time to act.”

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Write to Katy Steinmetz at katy.steinmetz@time.com.