“This action demonstrates that President Trump is committed to fixing the damage caused by Obamacare as soon as possible,” said Senator John Barrasso, Republican of Wyoming.

The order does not direct the Department of Health and Human Services to ease any particular aspect of the 2010 law, but it could result in a substantial weakening of one of its central features: the so-called “individual mandate” that requires most Americans to have health insurance or pay a tax penalty.

While the Obama administration allowed “hardship exemptions” to the mandate, the Trump administration could conceivably interpret the requirement in a more lenient way, so that more people would not be penalized.

Likewise, federal officials could be more receptive to state requests for waivers under Medicaid, the federal-state program that covers more than 70 million low-income people. A number of Republican governors and state legislators would like to charge higher premiums or co-payments than are now allowed. Some states want to provide a less generous, less expensive package of benefits, or require some able-bodied adults to engage in work activities as a condition of receiving Medicaid.