WASHINGTON — 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.