But only two hours after she introduced the bill, leaders of a more centrist group known as the New Democrat Coalition said Congress should initially focus on shoring up the Affordable Care Act, stabilizing insurance marketplaces and holding down prescription drug costs.

“We’re going to be very practical,” said Representative Kurt Schrader of Oregon, a chairman of the New Democrats’ health care task force.

Another lawmaker in that coalition, which has 101 members, said it might make more sense to allow people to voluntarily “buy into” Medicare or Medicaid.

That approach, said the lawmaker, Representative Kim Schrier, Democrat of Washington, “would not cause as many seismic effects” as the shift to a single-payer system.