On the campaign trail, Donald Trump’s proposal on health care was nebulously perfect. Obamacare — that is, the Affordable Care Act — would be gone, he told his cheering supporters, replaced by something cheaper, better and more expansive that wouldn’t be burdened by the hated word “Obama.”

When it came time to deliver on that promise, very early in his administration, the bill that was offered up was somewhat distant from that target. The American Health Care Act would actually see fewer people covered by a decade from now, independent analysis indicated, and costs would drop largely because those with the most expensive plans would stop getting coverage. Trump halfheartedly championed the bill even though it wasn’t his creation. When it collapsed, the exhalation from the White House was nearly audible.

The problem, though, is that the failure appears to have made any future significant changes trickier. New polling from The Washington Post and our partners at ABC News as well as a survey from NBC News and the Wall Street Journal makes clear that Trump’s base still wants Obamacare to be tossed out — but that it mostly opposes the most viable path toward doing so.

It’s still the case that three-quarters of the people who voted for him and three-quarters of Republicans overall want to see Obamacare repealed and replaced. The majority of Americans disagree, mind you, thanks to large majorities of Democrats and independents who think that it’s preferable to improve the existing law. Sixty-one percent of Americans overall hold that view.

The NBC-Journal poll saw a similar partisan split, with independents narrowly preferring to stop trying to repeal the bill when offered a repeal-or-not choice. Still, three-quarters of Republicans backed continuing the fight.

So. Fine. Trump’s base wants the repeal effort to move forward. How to accomplish it?

Somewhat remarkably, nearly half of Trump voters — more than Republicans overall — think that Trump should work with Democrats instead of or alongside conservative Republicans to come up with solutions. The number of Trump voters who think he should work with conservative Republicans only is still higher, but there’s a lot of support for a bipartisan approach.

The problem with that, of course, is that Trump was already trying to hammer out an agreement between conservatives in the House and more moderate representatives — it was just that those middle-ground members of the House were in his own party. The reason that he and House Speaker Paul D. Ryan (R-Wis.) could never get a majority of support on the AHCA was that there was enough opposition from both the far-right and center of his party to keep him from getting over the finish line. Trying to find middle ground between those conservatives — who generally want to gut the bill — and Democrats who broadly want to bolster it would be some magic trick.

What’s more, one of the proposals that’s moved to the center of the conservative focus on reforming Obamacare — removing the mandate that preexisting conditions be covered — is opposed by majorities across the political spectrum. Even a majority of Trump voters think that there should be a national standard to protect preexisting conditions.

The challenge with preserving those protections is that it is one of the main drivers of the cost of the program, which is why conservatives have focused on it. But it’s strongly supported. Seventy percent of Americans think the idea should be preserved.

Health-care experts say the Affordable Care Act is stable, but President Trump and congressional Republicans could push it over the cliff into a "death spiral." (Daron Taylor/The Washington Post)

Trump’s strategy, then, has been to Sherman-march his way through the issue, letting Obamacare fail (perhaps with a few unsubtle nudges) and then rebuild from the rubble. As it stands, though, that strategy bears its own risks. A majority of every group thinks that the better strategy is to make Obamacare work better while repeal efforts are underway — including well over half of those who voted for Trump last year.

That’s a Catch-22 for Republicans: Making Obamacare stronger, of course, will also reinforce its popularity, since it will be a better program. The program has seen a surge in popularity since the election as the threat of it being repealed loomed.

But repealing and replacing Obamacare necessitates having something viable to repeal and replace it with. So far, that’s been elusive for Republicans. And according to that NBC-Journal poll, that’s become apparent to American voters. In February, 31 percent of respondents said they had a “great deal” or “some” confidence in the Republican replacement bill. By this month, fully half of respondents said they had “little or no” confidence in it.

Trump’s vague promise of a universally better and cheaper program was always worth a good deal of skepticism. But the faltering effort to reform the health-care system earlier this year appears to have made his already-impossible goal somehow even more distant.