WASHINGTON — With the Supreme Court set to render judgment on President Obama’s health care law as early as Monday, the White House and Congress find themselves in a position that many advocates of the legislation once considered almost unimaginable.

In passing the law two years ago, Democrats entertained little doubt that it was constitutional. The White House held a conference call to tell reporters that any legal challenge, as one Obama aide put it, ‘‘will eventually fail and shouldn’t be given too much credence in the press.’’

Congress held no hearing on the plan’s constitutionality until nearly a year after it was signed into law. Representative Nancy Pelosi, then the House speaker, scoffed when a reporter asked what part of the Constitution empowered Congress to force Americans to buy health insurance. ‘‘Are you serious?’’ she asked with disdain. ‘‘Are you ­serious?’’

Opponents of the health plan were indeed serious, and so was the Supreme Court, which devoted more time to hearing the case than to any other in years.

A White House that had ­assumed that any challenge would fail now fears that a center­piece of Obama’s presidency may be partly or completely overturned on a theory that it gave little credence. The miscalculation left the administration on the defensive as its legal strategy evolved over the last two years.

‘‘It led to some people taking it too lightly,’’ said a congressional lawyer who like others involved in drafting the law ­declined to be identified before the ruling. ‘‘It shouldn’t strike anybody as a close call,’’ the lawyer added, but ‘‘given where we are now, do I wish we had ­focused even more on this? I guess I would say yes.’’

Looking back, Democrats said they had had every reason for confidence, given decades of Supreme Court precedents affirm­ing Congress’s authority to regulate interstate commerce, and lawyers who defend­ed the law said they had always taken the challenge seriously, even if politicians had not. But they underestimated the chances that conservative judges might interpret those precedents differently or discard them.

Adversaries said the law’s proponents had been too attentive to liberal academics who shaped public discussion.

‘‘There’s very little diversity in the legal academy among law professors,’’ said Randy E. ­Barnett, a Georgetown University law professor and a leading thinker behind the challenge. ‘‘So they’re in an echo chamber listening to people who agree with them.’’

David B. Rivkin Jr., who filed a challenge that was joined by 26 states, said that extended across party lines. ‘‘Nobody in Congress is interested in constitutional issues,’’ he said. ‘‘The Republicans on the Hill were no better than the Democrats. It really was very late in the game when Republicans realized there would be no policy deal and began to look at the constitutional issues.’’

And the Supreme Court may yet uphold the law, in which case the second-guessing in Washington will quickly transform into triumphant told-you-so’s. Pelosi, for one, has not retreated. ‘‘We’re ironclad on the constitutionality of the bill,’’ she told CBS this month. ‘‘I think we’ll be 6-3 in our favor.’’

Democrats were so sure from the start because the concept of requiring Americans to obtain insurance or pay a penalty had originally been ­advanced by conservatives to avoid government-run health care. The Constitution authorizes Congress to regulate interstate commerce, but critics ­argued that rather than regulate activity, the law regulated inactivity, in other words, the choice of some Americans not to purchase a health policy.

Thomas J. Perrelli, until recent­ly the associate attorney general, said that the legal team had taken the case seriously and that anyone who had not was misguided. ‘‘You had to know this was going to the ­Supreme Court,’’ he said, ‘‘and it would be one of the most ­important cases of the decade.’’

The issue came up briefly on the Senate floor when Democrats voted down a constitutional objection by Republicans. Days before final passage, White House and Justice Depart­ment lawyers sat down to map out a defense. Some in the room recalled being acutely aware of the danger. The White House assigned a new associate deputy attorney general, Robert Weiner, to coordinate defense.

The first lawsuits were filed the day Obama signed the plan into law in March 2010. By the end of January 2011, judges in Florida and Virginia had ruled it unconstitutional. Only then did the Senate and House hold hearings on its constitutionality, and the administration grew worried.

As cases moved to appeals courts, Neal Katyal, the acting solicitor general, personally took over, rather than wait until they reached the Supreme Court.

After some debate, ­Katyal decided to speed up the process rather than delay. The Department of Health and ­Human Services wanted the law resolved to prepare for full implementation in 2014. Katyal dropped procedural objections and asked for quick schedules.

He reformulated strategy to make a conservative case for the law, citing the Federalist ­Papers to argue that the founders saw the commerce clause as a broad tool when states could not solve problems.