But Republican leaders acknowledge that many Americans would struggle to pay for insurance without government help. The committee plan would offer a different kind of refundable tax credit: a flat subsidy, depending on the age of the insurance purchaser. Some conservatives see such a system as too profligate — Senator Rand Paul of Kentucky has called it “Obamacare-lite” — because it still pays some people more in financial assistance than they would otherwise pay in taxes. Those lawmakers tend to support plans that would lower people’s tax bills if they bought insurance, but not award them additional financial aid if they don’t pay much in income tax.

President Trump appeared to weigh in on this debate during his address to Congress on Tuesday, by offering an endorsement of “tax credits” as the funding mechanism.

Getting unstuck: The fate of the tax credit approach may come down to money. The Congressional Budget Office is working with committees to estimate how much the plan would cost and how many people it would cover. If the cost is deemed large or the number of Americans covered shrinks by a lot, compromise gets even less likely. But if the tax credits turn out to be inexpensive, the fights over the subsidy structure might become less heated.

The role of employer plans

Congressional Republicans are largely united in wanting to sweep away the many new taxes created by the Affordable Care Act. The law taxed drugs, health plans, medical devices, tanning salons, expensive health plans — and raised Medicare taxes on high earners. The plan would do away with all those taxes.

But without them, even a stripped-down Medicaid program and smaller tax credits start to get expensive. And finding a source of funding for the bill’s benefits is tricky in a caucus that tends to oppose any sort of tax increase.

The committee plan would find some money by limiting the tax exclusion for employer health benefits. Currently, neither employers nor their workers pay any taxes on money that goes toward health insurance. Limiting the money that can go to employer benefits tax-free would help provide tax assistance for people who buy their own coverage. Health economists also think that limiting the exclusion could help drive down health spending. But the employer tax exclusion is widespread and popular — and capping it is seen by some as a tax increase. That means that some members of Congress are ideologically opposed to the idea.

Getting unstuck: The Republican lawmakers who care about the federal deficit will have to find money from somewhere to make the math work, and capping the employer exclusion is the only proposal on the table. Using this method would allow them to brag about sweeping away Obamacare’s other taxes. But they’ll have to be willing to stomach complaints from constituents and employer groups.