A fleet of top Democratic lawmakers unveiled a bill Wednesday that would outlaw discrimination against lesbian, gay, bisexual, and transgender (LGBT) individuals in federal law, pitching their effort as the next step toward full LGBT equality.

"After years under a legal cloud, [marriage equality] is now the law of the land, but #LGBT discrimination is allowed to flourish," New York Sen. Chuck Schumer, the number three Democrat in the Senate, tweeted on Wednesday. "We must shine a light on injustice. #LGBT discrimination has no place in our housing, employment, and education laws."

The Full Equality Act of 2015 is being sponsored in the House by Rep. David Cicilline, D-Rhode Island, and in the Senate by Sens. Jeff Merkley, D-Oregon, Tammy Baldwin, D-Wisconsin, and Cory Booker, D-New Jersey. It would amend a number of existing federal laws to expand legal protections for LGBT individuals in arenas like employment, housing, and commerce.

Get Breaking News Delivered to Your Inbox

One provision likely to draw opposition from Republicans would guarantee LGBT people equal access to public accommodations, forbidding most U.S. businesses from discriminating against gay customers.

As the fight for same-sex marriage reached its culmination at the Supreme Court last month, Republicans were busy promoting religious freedom laws to safeguard the rights of businesses to decline to provide goods or services that would violate the owners' religious beliefs. It was a reaction, the GOP said, to recent criticisms and penalties directed at florists, restaurants, and other businesses that declined to cater to gay weddings.

The GOP has cited the Religious Freedom Restoration Act (RFRA), signed into law by then-President Bill Clinton in 1993, to justify its latest push for religious liberty. But that bill was designed to protect the rights of American Indians and other small religious groups to practice their faith free of federal interference. The legislation introduced Wednesday would clarify that RFRA cannot be used to sanction businesses' discrimination against LGBT customers.

In perhaps its most sweeping move, the bill would also add sexual orientation and gender identity to the list of classes protected under the 1964 Civil Rights Act, which would forbid businesses from discriminating against LGBT people in hiring, firing, or promotion practices. Religious schools, hospitals, and other institutions would continue to enjoy existing exemptions that allow them to consider religious beliefs in hiring practices if the employee in question will be doing work involving the practice of their faith.

22 states and the District of Columbia currently have laws protecting gay or transgender individuals from employment discrimination, but LGBT activists say the legal patchwork leaves too many Americans exposed to potential discrimination.

Gay couples nationwide "now have the opportunity to get married," Human Rights Campaign spokesman Adam Talbot told CBS News in June. "But in some instances, it will mean coming out publicly in their community at a certain time. So when they post their wedding photos at 10 a.m., their employer fire them at noon because of those photos, and their landlord can evict them at 2 p.m., because in most states in this country there's no statewide nondiscrimination law that protects them from that kind of action."

Additional protections in the bill would safeguard LGBT equality in housing, healthcare, public education, student loans, and even jury selection.

Some of the activists who were front-and-center in the push for marriage equality have signaled their support for proposals like the one introduced Wednesday.

"A top priority for our movement needs to be passing a federal civil rights law that would prohibit discrimination broadly on the basis of sexual orientation and gender identity," Freedom to Marry director and co-founder Evan Wolfson told CBS News.

Other activists, though, are leery of introducing such a bill in a Republican-controlled Congress. They fear the additional safeguards could simply be stripped from the bill - or worse, that the GOP could use the bill as a vehicle to chip away at existing civil rights protections.

"There is a very real possibility that amendments will be introduced on the Senate floor by the likes of Ted Cruz or Tom Cotton or a whole host of other right-wing lawmakers that not only strip the bill of its intended protections, but also gut the civil rights laws being amended," GetEQUAL co-founders Heather Cronk and Angela Peoples wrote in an op-ed in the Advocate magazine last month.