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The ruling is also sure to dominate on the Internet. A coalition of groups opposing the law led by the State Policy Network is using the hashtag #judgmentday to tweet about it, while supporters of the law such as Families USA and National Women’s Law Center say their hashtag will be #healthjustice.

As the hours ticked down Wednesday, the Obama administration and House Republicans each said they were confident they will prevail.

White House spokesman Jay Carney rattled off some of the most popular parts of the law — mandating that insurers cover young adults on their parents’ policy and that they offer preventive services without co-payments — while brushing off questions about what the administration plans do if the court overturns parts of it.

“I won’t, with just 20 hours left or so before we hear from the Supreme Court … speculate about hypothetical scenarios,” Mr. Carney told reporters. “We await the decision, as everyone does, and I can simply point you to what the HHS Secretary [Kathleen] Sebelius, has said … we are ready.”

Aware that the court could uphold the entire law, Republicans have been hedging their bets, saying they will work to repeal the entire law no matter what happens.

“We’ve made it pretty clear, and I’ll make it clear one more time,” said House Speaker John A. Boehner, Ohio Republican. “If the court does not strike down the entire law, the House will move to repeal what’s left of it.”

Some used the last-minute frenzy to score political points. The Democratic Congressional Campaign Committee blasted out an email with a fundraising plea from Patrick Kennedy. He is a son of the late Sen. Edward M. Kennedy, who championed the law but died shortly before Congress passed it in 2010.

The Club for Growth took the opportunity to slam U.S. Senate candidate Tommy G. Thompson, the former Republican governor of Wisconsin, for saying in the past that he would back some type of an insurance mandate. The group says it opposes Mr. Thompson because he is not fiscally conservative enough.

The court’s decision could leave both sides with mixed feelings, if it chooses to strike down the mandate but leave the rest of the law in place. But things will be more polarized if the justices either uphold the whole law or strike it all down — with each side hoping they will be the ones celebrating.

Mr. Kennedy said Cato hasn’t planned any after-parties, but there’s likely to be some merrymaking if things turn out as they hope.

“It’s safe to say if, in fact, the individual mandate is struck down, we’re going to be a pretty happy staff,” he said. “I anticipate there will be some staff out that day having a good time if the decision goes the way we hope.”