1st make Carter a progressive
Carter was in no way a full-throated progressive!!!
If anything, he was Reagan-Lite.
He was OK on civil rights, but very much into God and national defense.
IIRC his lukewarm support of the ERA doomed it to defeat in Congress.
OTOH, it may very well be it was impossible to make that bill pass, but I think it just needed a little nudge to become law. YMMV.
Also, keep in mind, Carter snuck in after a demoralized and bitterly divided primary campaign decimated any establishment candidates. Much like Clinton did in 1992 (also with scant support from Congress on the best of days!).
Gee, how history repeats itself, but I digress.
As to letting the GOP lame duck its way through to 1980, with the second or third president under its lackluster banner, you could possibly butterfly Raygun Ronnie and make a fatal split between the Libertarians, moderate GOP, and
evangelists all going their separate ways in a fratricidal bloodbath that would make Whigs spin in their graves.

I see it ushering in a spectacularly lackluster Era of Ill Feeling as Democrats no longer have significant external opposition where the Great Society dinosaurs and progressives start barracking over who inherits the keys to Congress and Presidency.
However, the Dem taking the helm in 1980 probably wouldn't be anyone really progressive or be in much better shape. I'm thinking Scoop Jackson, Mondale, or some other DNC figure that would NOT have let the worst domestic bits of the 1980's -hollowing out of industry, all the corporate restructuring shenanigans, insane govt borrowing and AIDS crisis go as far as they did.
OTOH would Scoop, HHH, or Mondale have pushed the USSR as hard with the SDI bluff, Pershing/ACM deployments, and/or supporting the Afghans and contras to end the Cold War?
Plus, much as I despised the hypocrisy of much of the Contract with America crowd in 1994, they hit a vein of genuine popular disgust with business-as-usual (Dem) politics in Congress. Move that ahead ten years if Dems are the only viable national party from 1980 to 1992.
I also see a much more active militia movement at the same time, b/c the right wing would NOT be anywhere in range of power with a much wider "liberal" consensus making them cry and whine in the corner about being ignored. IMO w/o Carter and Reagan giving the evangelicals much entree to DC, they stay marginalized much longer and radicalize more and get squished by the FBI as terrorists.