It now seems like a distant and even quaint memory, but earlier this year, Republicans published an “autopsy” into what went wrong in 2012, recommending that the party undertake changes to make it more tolerant and inclusive, with better outreach to Latinos and more sensitivity to young voters’ increasing acceptance of gay rights.

Now, with the GOP brand in the toilet in the wake of the shutdown crisis, it’s likely the House GOP won’t act on immigration reform this fall. And any day now, Republicans may be facing a big test on gay rights, too.

A Senate Democratic aide tells me that as early as next week, and certainly some time before Thanksgiving, the Senate will bring to the floor the Employment Non-Discrimination Act, which would bar discrimination based on sexual orientation in hiring by all but the smallest businesses.

The Senate health and education committee passed ENDA in July, with three Republicans voting for it: Mark Kirk, Lisa Murkowski, and Orrin Hatch. Roll Call’s David Hawkings notes that with the ascension of Cory Booker to the Senate, Dems now have 56 votes in favor of ENDA, and he adds that a number of GOP Senators are being targeted for lobbying, such as Rob Portman (who’s in favor of gay marriage), Kelly Ayotte, Pat Toomey, and Jeff Flake. There’s some last minute holding out by a couple red state Dems (as always), but it seems very likely that there will be at least 60 Senators to break the GOP filibuster.

The question will be, What happens in the House? Interestingly, gay rights advocates are hoping that the self-debilitating chaos that took hold of the GOP caucus during the shutdown fight could play in their favor. As Hawkings puts it:

LGBT advocates sense an opening to capitalize on efforts by the party establishment to grow their base in order to prevent a takeover by tea partyers and culture warriors, which could debilitate the GOP’s national prospects for years.

The idea that not evolving on gay rights could damage the Republican Party deep into the future is shared by Republican operatives. Here’s what the GOP autopsy said:

Already, there is a generational difference within the conservative movement about issues involving the treatment and the rights of gays — and for many younger voters, this issue is a gateway into whether the party is a place they want to be.

Polls show majorities support marriage equality. Gay marriage is legal in 14 states. And  in the wake of the Supreme Court decision that created a whole new legal framework for challenging gay marriage at the state level, same-sex couples and gay rights groups currently are pursuing lawsuits in 20 more states, according to Lamda Legal. So the culture continues to shift.

A stand against gay workplace discrimination should theoretically be easier than favoring gay marriage, because it doesn’t come freighted with the same cultural and religious implications. As Steve Benen, who hears a vote could come as early as this week, puts it:

A lot of Americans don’t know this, but under existing law, gay people can be fired from their jobs simply because of their sexual orientation. Discrimination on the basis of race, gender, or religion is illegal, but an employer could walk up to a gay employee this afternoon, declare, “I don’t like gay people so you’re fired,” and there’s literally nothing in federal law to prevent this happening. […]

If you’re a policymaker comfortable with federal anti-discrimination laws to protect women and minority groups, then you have no reason to oppose ENDA. Either you’re willing to tolerate employment discrimination or you’re not.

If Republicans stand in the way of ENDA, it will reinforce the sense of a party that is adamantly refusing to evolve along with the rest of the country and the culture, and deepen the perception that it remains hostage to its most hidebound, extreme and intolerant elements.