Republicans have not settled on the details or the timing of their replacement plan. The House speaker, Paul D. Ryan of Wisconsin, portrays repeal of the law not as an ideological crusade, but as a form of urgently needed relief.

“Insurance markets are collapsing,” Mr. Ryan said this week. “Premiums are soaring. Patients’ choices are dwindling.”

The House leadership aide said that repealing major provisions of the law was a priority for the first 100 days of the Trump administration. But, he said, the date that those provisions would actually disappear would be delayed, allowing a transition period as short as two years or as long as three or four years. During that time, Republicans plan to pass one or more replacement bills.

By giving people the choice to buy insurance, Republicans could end up dangerously skewing the health insurance market, Obama administration officials and insurance executives say. Sick people are more likely to sign up, they say, and there may not be enough healthy people paying premiums to cover the costs for those who are less healthy.

Under the Affordable Care Act, people who go without insurance are subject to tax penalties. The Internal Revenue Service says that more than eight million tax returns included penalty payments for people who went without coverage in 2014.

The House leadership aide said that lowering the cost of insurance was a much better way to encourage people to opt in.

“We would like to get to a point where we have what we call universal access, where everybody is able to access coverage to some degree or another,” the aide said. “Over the past six years, if you look at the experience we’ve had with the A.C.A. rollout, chasing coverage doesn’t necessarily yield great outcomes. You can have people going into an exchange, finding out that their pediatrician is no longer available to them.”