House Republican leaders would offer to help people buy insurance on the free market with a tax credit that, for some low-income households, could exceed the amount they owe in federal income taxes.
Some of the most conservative Republicans say the tax credit should not be more than the amount of taxes consumers owe. If the government makes payments to people with little or no tax liability, they say, that would amount to a new entitlement program, replacing one kind of government largess from President Barack Obama with another from Mr. Trump.
“Coming in as a Republican president with a new federal entitlement program?” asked Representative Dave Brat, a conservative Republican from Virginia. “That’s your first big move? You would have politicians bidding up the cost, adding to the financial problems of other entitlement programs like Medicare and Social Security.”
After the president’s speech, aides to the House speaker, Paul D. Ryan, crowed that they had the full backing of Mr. Trump for their health care plan.
But Mr. Trump was decidedly vague. He backed tax credits to buy insurance, but he did not clearly resolve the disagreement between Mr. Ryan and the most conservative Republicans.
“We should help Americans purchase their own coverage through the use of tax credits and expanded health savings accounts,” Mr. Trump told a joint session of Congress.
The details of the tax credit could make a substantial difference to consumers. If a family is eligible for a $3,000 tax credit to buy insurance and owes $1,000 in federal income taxes, should it get only $1,000? Or should it get the full $3,000?
Most tax breaks reduce the amount owed to the government. A refundable tax credit can also result in payments from the government: If the credit exceeds a person’s tax liability, the government pays him or her the excess.
“I think refundable tax credits are just another word for subsidies,” said Senator Rand Paul, Republican of Kentucky.
Defenders of refundable tax credits say they are needed to make insurance affordable to people who pay little or no taxes.
“Otherwise, they’re useless,” said Representative Chris Collins of New York, one of Mr. Trump’s top supporters in Congress. “What good’s a tax credit for folks who don’t pay taxes?”
In fact, for those who cannot pitch in much of their own income, even a refundable tax credit is not likely to be enough to pay for a health insurance policy, Democrats say. That is one reason the Republican alternative is not likely to cover as many people as the Affordable Care Act.
At the meeting on Wednesday, several Republican senators expressed concern that the tax credit proposed by House leaders would be available even to people with high incomes who did not need federal assistance.
Earlier, Representative Kevin Brady, Republican of Texas and head of the Ways and Means Committee, said the credit would be a way to provide more equity in the tax code by creating a tax break for people who buy insurance on their own, similar to the break already available to people who get insurance through the workplace.
He predicted that Republicans would overcome their divisions.
“Rather than using his speech to divide Republicans,” Mr. Brady said, “it’s really an opportunity for us to sit down and work through what remaining differences there are, and I’m confident we can.”
Mr. Brady and another architect of the House plan, Representative Greg Walden of Oregon, the chairman of the Energy and Commerce Committee, huddled with Republican senators on Wednesday. But lawmakers left the meeting with many unanswered questions and were not ready to endorse the House plan.
The fractures among Republicans have been on display in the past few days. On Monday night, three senators — Mr. Paul, Mike Lee of Utah and Ted Cruz of Texas — posted on Twitter in support of what they called #FullRepeal.
“If we fail to honor our commitment to repeal Obamacare, I believe the consequences would be, quite rightly, catastrophic,” Mr. Cruz said on Wednesday.
The leaders of two groups of House conservatives, the Republican Study Committee and the House Freedom Caucus, also came out against a draft of the health care legislation that became public during last week’s congressional recess. The groups have more than enough members to thwart House leaders’ plan if they are determined to do so.
Senator James Lankford, Republican of Oklahoma, likened the leadership’s tax-credit proposal to the earned-income tax credit, which supplements the wages of low-income workers. There has been “a tremendous amount of improper payments” in that program, he said.
Other Republican skeptics include Senators Thom Tillis of North Carolina and Lindsey Graham of South Carolina. “There are other ways you can address that segment of the population,” Mr. Tillis said of the working poor with little or no income tax liability.
Some Republicans are also concerned about the possibility of requiring workers to pay taxes on the value of employer-sponsored coverage exceeding certain thresholds. Employers and labor unions strenuously oppose such a move, which would affect people in the most expensive health plans and is similar in purpose to a provision of the existing law. Both measures are designed to curb overuse of health care and to help pay for the broader measures.
“I don’t think it’d go over very good in the Senate,” Senator Charles E. Grassley, Republican of Iowa, said last week.
Then there is the issue of Medicaid. Lawmakers from states that expanded Medicaid under the Affordable Care Act face pressure back home — in some cases, from Republican governors — to oppose sharp cuts to the generous federal funding that those states are receiving.
Senator Lisa Murkowski, Republican of Alaska, which has expanded eligibility for Medicaid under the health care law, said she wanted to be sure that her state could retain the expansion if its legislature wanted to do so.
“Alaska should have that option,” she said.