The easiest way for the Trump administration to undermine the health law would be to stop defending a lawsuit brought by the House of Representatives. That suit said that the Obama administration lacked the authority to pay certain Obamacare subsidies. A lower court ruled for the House, meaning that by simply withdrawing from the appeal, the Trump administration could start a process to eliminate those subsidies and cause a collapse of the insurance market. Mr. Trump’s order said nothing about that policy choice.

Another important area of discretion has to do with exemptions to the law’s unpopular individual mandate to obtain insurance. Under the law, all Americans who can afford it are expected to obtain health insurance, unless they have experienced some hardship that would make it impossible. People who feel there has been such a hardship can apply for an exemption, and employees in the Department of Health and Human Services and the Internal Revenue Service can decide on their case. Under a Trump administration, it might become easier to claim hardship and get out of the requirement to buy insurance.

But people seeking those exemptions will still have to apply for them, in writing, and can do so only at particular times of the year. Current law requires them to provide documentation supporting their claim that they have recently filed for bankruptcy, for example, or been evicted, and they must legally attest to their honesty. The Trump administration could create new categories of hardship, but that would take time. And rules that effectively eliminate the requirement would almost certainly result in litigation.

“It’s not a hardship to have to comply with the law, almost by definition,” said Timothy Jost, a professor of law at Washington and Lee University. Mr. Jost, who supports the health law, has examined the underlying regulations in detail.

Defanging the individual mandate could have significant consequences for the individual insurance markets. If fewer healthy people buy insurance, the costs of insuring everyone else will rise, leading insurance companies to raise prices or flee the market.

Last week, the Congressional Budget Office published its estimate of what would happen under a law that eliminated the mandate and some other provisions: 18 million people would lose their insurance next year alone. It’s possible that insurers will look at the language of the order and get skittish, setting off a market collapse next year. But the order itself doesn’t yet change any rules. The health and human services department and the I.R.S. will have to take further action.