House and Senate negotiators thrashing out differences over a major tax bill are likely to eliminate the insurance coverage mandate at the heart of the Affordable Care Act, lawmakers say.

But a deal struck by Senate Republican leaders and Senator Susan Collins of Maine to mitigate the effect of the repeal has been all but rejected by House Republicans, potentially jeopardizing Ms. Collins’s final yes vote.

“I don’t think the American people voted for bailing out big insurance,” said Representative Dave Brat, Republican of Virginia, who opposes a separate measure to lower insurance premiums that Ms. Collins thought she had secured.

The sweeping tax overhaul approved Saturday by the Senate would eliminate penalties for people who go without insurance, a change not in the tax bill passed last month by the House. But the House has voted many times to roll back the mandate, most recently in a bill to dismantle the Affordable Care Act, and House members were enthusiastic about going along.

“Mandating people to buy a product was a bad idea to begin with,” said Representative Rob Woodall, Republican of Georgia. “We made people do something that was supposed to be good for them. But they are telling us by the millions how much they dislike the mandate.”

The individual mandate was originally considered indispensable to the Affordable Care Act, a way to induce healthy people to buy insurance and thus to hold down insurance premiums for sicker customers. The Obama administration successfully defended the mandate in the Supreme Court. But recent economic research suggests that the effect of the mandate on coverage is somewhat smaller than previously thought.

With little more than a week remaining until the annual open enrollment period ends, 3.6 million people have selected health plans for 2018 in the 39 states that use the federal marketplace, the Trump administration reported Wednesday. That is 22 percent higher than at this point last year, despite uncertainty about the mandate’s future and efforts by Republicans and the administration to undermine the law.

But because the sign-up period is only half as long, it appears likely that enrollment will end up lower than in the last period.

Without a mandate, some healthy people are likely to go without coverage, leaving sicker people in the market, and prices are likely to rise more than they otherwise would. The Congressional Budget Office said last month that repealing the individual mandate would increase average premiums on the individual market about 10 percent, and it estimated that the number of people without health insurance would rise by 13 million.

Regardless, the requirement has proved to be one of the most unpopular parts of the 2010 law, and House Republicans were happy to see it go. Representative Richard Hudson, Republican of North Carolina, called the Senate provision “a great move.”

The repeal also frees up money that Congress can use to reduce tax rates. The budget office said it would save the federal government more than $300 billion over 10 years — mainly because fewer people would have Medicaid or subsidized private insurance.

The mandate repeal’s effect on health insurance markets did concern Ms. Collins, and to win her vote for the Senate tax bill, the Senate majority leader, Mitch McConnell of Kentucky, offered her a deal, in writing: He would support two bipartisan bills to stabilize markets and hold down premiums, in the absence of the individual mandate.

One bill would provide money to continue paying subsidies to insurance companies in 2018 and 2019 to compensate them for reducing out-of-pocket costs for low-income people. President Trump cut off the “cost sharing” subsidies in October, more than a year after a federal judge ruled that the payments were unconstitutional because Congress had never explicitly provided money for them. The payments would resume under this measure, drafted by Senators Lamar Alexander, Republican of Tennessee, and Patty Murray, Democrat of Washington State.

The second bill would provide $5 billion a year for grants to states in 2018 and 2019. States could use the money to help pay the largest health claims, through a backstop known as reinsurance, or to establish high-risk pools to help cover sick people.

Ms. Collins has released a copy of her agreement with Mr. McConnell in which he pledged to support passage of the two measures before the end of the year. His signature was displayed prominently at the top of the first page. But the deal has landed with a thud in the House, where Republicans appear loath to support legislation that they view as propping up a health law that they have pledged to repeal.

“Our members wince at voting to sustain a system that none of them supported,” said Representative Tom Cole, Republican of Oklahoma.

The Senate could attach the Alexander-Murray legislation to a government funding measure, hoping that Republicans in the House would be willing to swallow it as part of a measure to avoid a government shutdown. But Mr. Cole said House Republicans would be “very offended” at such an approach.

“I don’t think we’re in the mood to be blackmailed by anybody,” he said.

Mr. Brat, a member of the conservative Freedom Caucus, assailed the deal with Ms. Collins as an example of horse trading that is characteristic of the Washington swamp that he said voters had repudiated.

Likewise, Representative Mark Walker of North Carolina, the chairman of the conservative Republican Study Committee, said of the Alexander-Murray bill, “There’s no appetite for that over here.”

Ms. Collins said on Wednesday that she believed the House would “take a serious look” at the two bills intended to hold down insurance premiums and that Mr. Trump, in several recent meetings, had assured her that he also supported those bills.

“I don’t think this effort is over by any means,” Ms. Collins said.

For Democrats, eliminating the insurance mandate penalties provides yet another reason to oppose the tax bill.

“The individual mandate is at the heart of the Affordable Care Act,” said Representative James E. Clyburn, Democrat of South Carolina. “Repealing it, as the G.O.P. tax scam does, is a deliberate attempt to undercut the law, create chaos in the health insurance marketplaces, increase premiums and decrease choice and coverage.”

Ms. Murray indicated that even if Ms. Collins secures her deal, Democrats would remain steadfast.

“Our bill, the Alexander-Murray bill, was designed to shore up the existing health care system,” not to “solve the new problems in this awful Republican tax bill,” she said.

Meanwhile, the damage to the Affordable Care Act may already have been done. Daniel Bouton, an enrollment counselor in Dallas, said he worried that the Trump administration’s decision to cut advertising for open enrollment had prevented millions of people from learning about the shortened sign-up period. He also said that the Senate’s recent vote to undo the individual mandate as part of its tax bill would discourage people from signing up.

“You’re going to have people who say, ‘Well, perfect, I don’t have to buy insurance anymore,’” Mr. Bouton said.