WASHINGTON — Congressional Republicans, meeting behind closed doors this week in Philadelphia, expressed grave concerns about dismantling the Affordable Care Act on the urgent timetable demanded by President Trump, fretting that, among other things, they could wreck insurance markets and be saddled with a politically disastrous “Trumpcare.”

An audio recording of a session at their annual retreat, obtained by The New York Times, shows Republicans in disarray, far from agreement on health policy, and still searching for something to replace former President Barack Obama’s health care law. While their leaders called for swift action to rescue consumers from the Affordable Care Act, some backbench Republicans worried about potential pitfalls.

“We had better be sure that we are prepared to live with the market being created,” said Representative Tom McClintock of California, because “that’s going to be called Trumpcare.”

He added, “Republicans will own it lock, stock and barrel, and we’ll be judged on that.”

When Democrats were writing the Affordable Care Act seven years ago, their primary goal was to provide health insurance to more people, an ambition that the Obama administration went to great lengths to fulfill as it enrolled millions of people in Medicaid or private health plans.