Details of the strategy are in flux, and there are disagreements among Republicans about how to proceed. In the House, the emerging plan, tightly coordinated between Mr. Ryan and Mr. Pence, is meant to give Mr. Trump’s supporters the repeal of the health law that he repeatedly promised at rallies. It would also give Republicans time to try to assure consumers and the health industry that they will not instantly upend the health insurance market, and to pressure some Democrats to support a Republican alternative.

“I don’t think you have to wait,” Representative Kevin McCarthy of California, the majority leader, told reporters this week. “I would move through and repeal and then go to work on replacing. I think once it’s repealed, you will have hopefully fewer people playing politics, and everybody coming to the table to find the best policy.”

Under the plan discussed this week, Republicans said, repeal will be on a fast track. They hope to move forward in January or February with a budget blueprint using so-called reconciliation instructions, which would allow parts of the health care law to be dismembered with a simple majority vote, denying Senate Democrats the chance to filibuster. They would follow up with legislation similar to a bill vetoed in January, which would have repealed the tax penalties for people who go without insurance and the penalties for larger employers who fail to offer coverage.

That bill would also have eliminated federal insurance subsidies, ended federal spending for the expansion of Medicaid, and barred federal payments to Planned Parenthood clinics.

But in the Senate, Republicans would need support from some Democrats if they are to replace the Affordable Care Act.

The budget reconciliation rules that would allow Republicans to dismantle the Affordable Care Act have strict limits. The rules are primarily intended to protect legislation that affects spending or revenues. The health law includes insurance market standards and other policies that do not directly affect the budget, and Senate Republicans would, in many cases, need 60 votes to change such provisions.