Sen. Mike Lee (R-Utah), seen in an April 2014 file photo, is leading the push among Senate Republicans to respond to the Supreme Court's gay marriage ruling. (AP Photo/Rick Bowmer)

Three weeks after the Supreme Court declared same-sex marriage a constitutional right, conservative lawmakers continue pressing to have Congress weigh in with a response — even as top Republican leaders show little stomach for putting divisive social issues on the front burner.

Reversing the ruling would mean pursuing a constitutional amendment that most anti-gay-marriage lawmakers admit will be a long-term -- and uphill -- project. In the short term, they are instead pressing for a more modest measure, the "First Amendment Defense Act," that would protect individuals or groups who believe same-sex marriages are immoral from government sanction.

The House version has garnered 124 co-sponsors, while the Senate companion has 34 cosponsors. While neither has enough support at this point to guarantee passage, the bills enjoy wide support among conservatives who have proven influential in setting the congressional agenda.

[Here are the key excerpts on religious liberty from the Supreme Court’s decision on gay marriage]

"Individual Americans, of course, may differ in their views about the definition of marriage; they may differ in their views about how this decision should have been reached," Sen. Mike Lee (R-Utah), author of the Senate bill, said at a Thursday press conference. "But I do think Americans are overwhelmingly united in their belief that religious freedom needs to be protected and that neither a person nor any group of people ought to be subject to government retaliation against based on their religious beliefs. ... That's why we're pushing this bill."

The First Amendment Defense Act is not as sweeping as the controversial state laws passed in Indiana, Arkansas and elsewhere that created a right for private businesses to deny their goods or services to gay people or to same-sex couples. The bill is instead focused on actions the government may take — in particular, potentially revoking the tax-exempt status of churches and nonprofit religious groups or denying them government grants, contracts or jobs. Last week, Kansas Gov. Sam Brownback issued an executive order making similar provisions in his state.

[Kansas governor: state can’t punish religious groups over same-sex marriage objections]

The bill provides that the federal government "shall not take any discriminatory action against a person, wholly or partially on the basis that such person believes or acts in accordance 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."

On Thursday, Lee and a handful of House members all cited the April 28 oral argument in the Supreme Court gay marriage case as prompting the legislation. There, Justice Samuel A. Alito Jr. asked Solicitor General Donald B. Verrilli Jr. about a precedent dating from 1983, where the Supreme Court held that the IRS was free to revoke the tax-exempt status of Bob Jones University because it banned interracial relationships.

"So would the same apply to a university or a college if it opposed same-sex marriage?" Alito asked.

Replied Verrilli, "I don't think I can answer that question without knowing more specifics, but it's certainly going to be an issue. I don't deny that. ... It is going to be an issue."

Rep. Raul Labrador (R-Idaho), the lead House sponsor, said Verrilli's comment proves there is a need for legislation. "All Americans should be free to believe and act in the public square based on their beliefs about marriage without fear of government retaliation or penalty," he said. "This is a great bill that all conservatives, libertarians, Democrats, Republicans should get behind, that could generate support in both parties and that can actually pass both houses of Congress."

And yet: House Speaker John A. Boehner (R-Ohio) declined to commit Thursday to bringing the First Amendment Defense Act, or anything else dealing with the aftermath of the gay marriage ruling, to the House floor. "A number of members have concerns about issues that it raises and how they might be addressed," Boehner said of the Supreme Court ruling. "But no decision has been made on how best to address these."

The House bill has been referred to two committees; neither has yet moved to consider it. Capitol Hill aides suggest that Republican leaders in both houses are wary of wading into the gay marriage debate so quickly after the court decision, and the fact that the lead sponsors of the bills, Labrador and Lee, have reputations for needling party leaders does not help.

[GOP moderates ready intraparty battle over religious freedom bill]

But the bill got the key backing of several leading conservative members this week, with Majority Whip Steve Scalise (R-La.) signing on as a cosponsor and Reps. Bill Flores (R-Texas) and Jim Jordan (R-Ohio), leaders of the Republican Study Committee and the House Freedom Caucus, respectively, endorsing the bill at Thursday's press event. The united front among conservatives could help push the bill to the House floor.

Equal-rights advocates are opposing the bill, saying it opens the door to discrimination against people in same-sex marriages by federal contractors who are now barred from discriminating through executive order. They also warn that gay people won't be the only ones who could be affected: a teacher at a private school receiving federal funding could be fired after having a child out of wedlock, they say — thus violating beliefs concerning whether "sexual relations are properly reserved" for traditional marriage.

Freedom for All Americans, an advocacy group pushing for stronger anti-gay-discrimination laws, called the First Amendment Defense Act "a broadly written bill that would allow individuals and organizations to discriminate against millions of Americans — including LGBT people, single mothers, unmarried couples, same-sex couples and others — based on their marital status."

[The freedom of religion argument could actually make gay marriage opponents more tolerant]

Thus far, only one Democratic lawmaker — Rep. Daniel Lipinski of Illinois — has co-sponsored either bill. Among Democrats, skepticism abounds: Sen. Richard Blumenthal (D-Conn.), a Judiciary Committee member and former state attorney general, said Thursday he was as yet unconvinced the bill was necessary.

"Certainly religious liberty is enshrined in the Constitution, so it deserves protection, but whether a statute is necessary, I'm not sure," he said. "Having argued four cases in the United States Supreme Court, I'd be loath to initiate legislation based on chance remarks made by an advocate in the heat of an argument."