Republicans in the Senate breathed a sigh of relief Tuesday as President Donald Trump backed away from his push to bring forward a GOP health care plan in the next two years. But their relief is ill-founded, and no matter what Trump does, it’s hard to see how they aren’t completely cornered on the health care issue.

They’re the quintessential dog who caught the truck, stuck yelping at a juggernaut that they have no means of actually taking on.

The latest chapter in the saga began last week when the Trump administration announced it would no longer defend Obamacare in court, instead taking the position that a lawsuit making its way through the courts should invalidate the law in its entirety. The lawsuit is seen as a longshot, but one federal judge has already ruled against the health care law, and the chance that it could make its way to the Supreme Court and kill Obamacare for good is considerable. So Trump announced that his party would move forward with a new push to repeal and replace Obamacare, an effort that failed in 2017 after the party had run on the pledge for nearly seven years.

But Trump backtracked Monday night, saying that the party will have a “really great HealthCare Plan with far lower premiums” and that it will pass it in “right after the Election” in 2020. (One wonders why they didn’t pass it in 2017!) Senate Majority Leader Mitch McConnell said Tuesday that he told the president that the health care push is dead in the Senate because the Democrat-controlled House of Representatives wouldn’t pass a GOP plan, triggering Trump to abandon his plans.

Politico reported that GOP senators had told Trump a health care push could drive “his party off an electoral cliff by forcing Republicans to take ownership of the health care issue.”

But the truth is that the Republicans do own the health care issue — probably any party in power would. For the GOP in particular, though, its “repeal and replace” Obamacare dreams have crumbled, even after all of the party and Trump’s grand promises. That means whatever complaints voters have about their health care in 2020 as they go to the polls, they can blame the Republicans’ failed promises.

The legal efforts to nullify Obamacare only make this threat of electoral backlash worse. Under Trump, the number of the uninsured has already risen by 7 million, according to recent data — if Obamacare were nixed, that number would rise many millions more.

This would be calamitous — and the fact that the Trump administration threw its weight behind the lawsuit seeking to end Obamacare could be devastating for Republican elected officials.

“If he wins in court, that Obamacare’s unconstitutional. I think it’s better than 50/50. What do we do in 2020?” Sen. Lindsey Graham (R-SC) told Politico. “Somebody needs to be thinking about that.”

But there’s no way out of this pickle. The complaints people have about health care is that it’s too expensive, of too low quality, or it’s not accessible at all. The core Republican belief about health care is that the government must become less involved in health care — but there’s no way to do this without make people’s plans worse, more expensive, and less accessible.

GOP lawmakers have long seemed to believe that there is some clever scheme cooked up by a wonk in a backroom that would involve both less government involvement in health care and policy outcomes that voters would love. But they didn’t have that solution in 2017 — all their plans would have resulted in significant coverage losses — and they don’t have that solution now, because it doesn’t exist.

If Republicans do nothing, Democrats will run against their failure to improve health care. If they move forward with a plan that would make health care worse, Democrats will run against that. And if they allow the courts to destroy Obamacare, Democrats will run to restore coverage to millions. And voters largely trust that Democrats on the health care issue more than they do Republicans — which is a major part of the reason Democrats won back the House in 2018.

There is one option for Republicans out of their dilemma: pass legislation that would actually improve health care in the United States. But that’s the one option they never seem to consider.