Republicans in Congress are worried the Supreme Court will hand them a major headache this month if it rules against the federal health insurance exchanges in more than 30 states, ending subsidies for millions of people.

While the Affordable Care Act remains broadly unpopular, two new polls show a majority of Americans don’t want to do away with its subsidies, a core component of the law.

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This poses a conundrum for Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellOcasio-Cortez to voters: Tell McConnell 'he is playing with fire' with Ginsburg's seat McConnell locks down key GOP votes in Supreme Court fight Video shows NYC subway station renamed after Ruth Bader Ginsburg MORE (R-Ky.) and Speaker John Boehner John Andrew BoehnerLongtime House parliamentarian to step down Five things we learned from this year's primaries Bad blood between Pelosi, Meadows complicates coronavirus talks MORE (R-Ohio). They are under pressure from colleagues up for reelection in swing states and districts to extend the subsidies, at least temporarily, if the court strikes them down. But doing so would risk a backlash from the conservative base.

The Supreme Court is expected to hand down its decision in King v. Burwell, which could strip 6.4 million people of health insurance subsidies, in late June.

States that would be hardest hit by a ruling against the law include the Senate battlegrounds of Illinois, North Carolina, Ohio and Wisconsin.

“The politics of the King vs. Burwell case are extremely treacherous and tricky for Republicans because if the subsidies are thrown out by the court, Republicans are in the position of having to create a fix that would be seen as a problem by their most conservative supporters,” said John Ullyot, a GOP strategist and former senior Senate aide.

A new Washington Post/ABC News poll found that a majority of the public, 55 percent, does not want the court to block federal subsidies for people in states that have not set up their own exchanges. Only 38 percent said they wanted the subsidies ended.

“It does create a political problem for the GOP because there could be millions of people who got health insurance as a result of ObamaCare who lose it,” said Darrell West, director of governance studies at the Brookings Institution.

“There’s a chance Republicans will get more of the blame because they’re in control of the House and Senate. Unless they can produce legislation, the blame will rest in their corner.”

Democrats feel confident that Republicans will be on the losing end if the court strikes down the subsidies. While congressional Republicans have publicly discussed five plans to respond to the ruling, President Obama and Democrats have not unveiled anything.

“It’s a problem for all the people affected by the loss of the subsidies and it’s a problem for Republicans. The potential solution, as the president said, is a very easy and simple one,” said a senior Democratic aide.

Obama said Monday at a news conference ahead of a Group of Seven summit in Germany that Congress could avoid any disruption in the subsidies by passing a “one-sentence provision” clarifying the federal government’s authority to set up exchanges.

But Republicans have rejected that idea and have been debating various stopgap plans that could serve as bridges between the court’s ruling and the 2016 elections.

Sen. Ron Johnson Ronald (Ron) Harold JohnsonGOP set to release controversial Biden report Democrats fear Russia interference could spoil bid to retake Senate The Hill's Morning Report - Sponsored by The Air Line Pilots Association - White House moves closer to Pelosi on virus relief bill MORE (R), who faces a tough reelection in the swing state of Wisconsin, has proposed legislation to extend subsidies until August 2017 and repeal the Affordable Care Act’s requirements to buy and provide insurance. Thirty-one Republican senators have co-sponsored the measure, including McConnell.

“My bill is a transition piece of legislation that will allow the American people a voice in what our health care system will look like beyond the 2016 election,” Johnson said in a statement. “It acknowledges political realities by preventing turmoil and disruptions should the Supreme Court rule subsidies cannot be paid through federal exchanges.”

Sen. Ben Sasse (R-Neb.) has floated legislation that would restructure the law’s subsidies and wind them down over the course of a year and a half.

If McConnell and Boehner John Andrew BoehnerLongtime House parliamentarian to step down Five things we learned from this year's primaries Bad blood between Pelosi, Meadows complicates coronavirus talks MORE opt to pursue these options, or something similar, it will provoke a fight with the party’s conservative base, a dangerous prospect heading into an election year.

“Our basic approach to this is, first of all, Congress shouldn’t overreact. You see some overreaction out there; the Johnson bill is a good example of that,” said Dan Holler, the communications director at Heritage Action for America.

“We think it’s a really dangerous step if you’re basically refunding ObamaCare. It’s not something the Republican conference should be doing,” he added. “Anything that gets at a straight extension of the subsidies is a nonstarter with conservatives.”

Senate Republican sources say McConnell would prefer not to deal with the political mess if he doesn’t have to.

Senate Republican Policy Committee Chairman John Barrasso John Anthony BarrassoMurkowski: Supreme Court nominee should not be taken up before election Battle lines drawn on precedent in Supreme Court fight Sunday shows - Ruth Bader Ginsburg's death dominates MORE (Wyo.), Finance Committee Chairman Orrin Hatch Orrin Grant HatchBottom line Bottom line Senate GOP divided over whether they'd fill Supreme Court vacancy MORE (R-Utah) and Health, Education, Labor and Pensions Committee Chairman Lamar Alexander Andrew (Lamar) Lamar AlexanderMcConnell locks down key GOP votes in Supreme Court fight Alexander backs vote on Trump Supreme Court nominee: What Democrats 'would do if the shoe were on the other foot' Toobin: McConnell engaging in 'greatest act of hypocrisy in American political history' with Ginsburg replacement vote MORE (R-Tenn.) are leading a working group that has met since January to explore legislative options.

In a March op-ed published in The Washington Post, Barrasso, Hatch and Alexander called for providing financial assistance to help Americans keep their coverage for a “transitional period” and giving states more flexibility to create more competitive health insurance markets.

But so far McConnell has made no effort to rally the conference behind one plan.

“I don’t get the sense there’s a concerted effort to distill those messaging points into a substantive legislative proposal that the conference would rally around,” one senior GOP aide said of the trio’s plan.

McConnell on Monday declined to discuss the details of the Republican backup plan, saying only that his party would be ready if the Supreme Court rules against the healthcare law.

“We’ll have a plan that makes sense for the American people,” he said during an interview on “The Joe Elliott Show.”

“If the plaintiff is successful, it will require some addressing of the issue, and if that were to happen we’ll be ready to announce our proposal.”

Don Stewart, McConnell’s spokesman, criticized Obama for having no contingency plan in case the court rules against the subsidies.

“Unlike the Obama administration, which has no plan, Republicans are working to protect families from the consequences of ObamaCare,” he said.

Jordain Carney contributed.