The law’s most popular provision is protections for people with pre-existing medical conditions, but it includes much more, such as health insurance exchanges where people can buy private coverage with subsidies, an expansion of Medicaid and requirements for what insurance must cover, from emergency services to prescription drugs.

The appeals court panel could decide to partly reverse Judge Reed O’Connor of the Federal District Court in Fort Worth, affirming that the mandate that most Americans have health insurance is unconstitutional but rejecting Judge O’Connor’s ruling that the rest of the law cannot stand without it. That would cause barely a ripple, because the tax penalty for not having insurance was reduced to zero in the 2017 tax overhaul and the effects have been negligible.

But a ruling that upheld his decision in full, or even one that said the mandate and pre-existing condition protections had to go, would send shock waves through the health care and political systems. Either outcome would probably play into Democratic hands, especially in contests against vulnerable Republicans like Senators Martha McSally of Arizona, Cory Gardner of Colorado, Susan Collins of Maine and Thom Tillis of North Carolina.

Republicans are not conceding that possibility. Asked how a ruling against the law might affect members of the party seeking re-election, the spokesman for the House Republican campaign arm, Chris Pack, said: “Both Democrats and Republicans oppose Obamacare. The only difference is that Democrats want to replace it with socialized single-payer health care that makes private health insurance illegal.”

In fact, most Democrats would welcome a renewed debate over the Affordable Care Act. Many Democrats in Congress have resisted Medicare for all; instead they have sought to shore up the existing health law and trap Republicans on pre-existing conditions. Senator Chuck Schumer of New York, the Democratic leader, intends to force a floor vote as soon as next week on a resolution to overturn a Trump rule that lets states promote skimpy-but-inexpensive insurance plans that do not meet the law’s coverage standards.

The vote, Mr. Schumer said Tuesday on the Senate floor, “will present our Republican colleagues with a choice: whether to protect Americans with pre-existing conditions or not to protect them.”

Mr. Trump is in a box on health care, the issue that registers as a top priority for voters in poll after poll. He wants deals on ending surprise medical bills and lowering prescription drug prices, but the Senate and House are far apart on what drug price legislation they would agree to, and impeachment proceedings could derail any chance of bipartisan measures.

Public support for the health law remains high, driven in part by swing voters. And few Americans believe Mr. Trump will offer details of a new health care plan before the end of the year, according to a Kaiser poll released this week. They also doubt any plan he releases would offer “better care at lower costs,” as he has promised.

Alex M. Azar II, the secretary of health and human services, has repeatedly played down the importance of expanding coverage to the remaining uninsured; instead, he has said, Mr. Trump wants to improve the health care system for all Americans. His efforts thus far have mostly been directed at discrete groups of patients: a plan to reduce new H.I.V. infections by 75 percent over five years, for example, and another to move people with advanced kidney disease to home-based, instead of clinic-based, dialysis.

At oral arguments before the appeals court panel in July, a lawyer from the Justice Department indicated the Trump administration would seek a stay if the panel upheld Judge O’Connor’s decision. The losing side could appeal directly to the Supreme Court, increasing the chances of a ruling or at least oral arguments before that court in the final months of the presidential campaign. Alternatively, it could first ask for a hearing by the full appeals court, which would slow down the process.

The appeals panel could also send the case back to Judge O’Connor to reconsider, an option that August Flentje, a lawyer for the Justice Department, embraced during oral arguments. That would also draw out the court fight.

When the six-week open enrollment period starts next month, there will be more insurers offering plans through the Affordable Care Act markets. Premiums have stabilized, too, after a few years of price increases. But it will be a much lower-profile effort than in past years; the Trump administration has cut the budget for both advertising and enrollment help. As a result, a court ruling against the law would paralyze open enrollment if people assume there is no use buying or renewing coverage under a law that was ruled unconstitutional, and if no effort is mounted to counter that misunderstanding.

“It will require a doubling down, a dramatic increase in education — which is exactly the opposite of what this administration has done,” said Leslie Dach, executive director of Protect Our Care, a consumer advocacy group aligned with Democrats. “Someone will need to educate people that low-cost, quality health insurance is still available to them.”