If the administration loses its argument, one early strategy is to run squarely against the Supreme Court. Democrats believe that Mr. Obama could fashion himself as a modern-day Franklin D. Roosevelt, trying to convince voters that a majority of the justices are in the pocket of the Republicans. A Democratic senator on Wednesday referred to that as the “martyr strategy.”

That approach, while galvanizing for Democrats, could also unify conservatives who have been slow to embrace Mr. Romney, in part because of his record on health care…

Despite suggestions from some Democratic activists that a ruling against the administration could energize the party and place the burden of finding a national health care solution on the Republicans, a loss at the Supreme Court would undoubtedly be significant for Mr. Obama. A decision to strike down the mandate or the entire bill would give greater legitimacy to the broader conservative argument that Mr. Obama has been expanding the size and reach of the federal government beyond what the Constitution allows.

One Democratic adviser compared it to “a bad bloody nose” that would bleed for days or weeks. The television advertising, particularly in an era of unlimited donations to “super PACs” lining up against Mr. Obama, would be “a disaster,” another Democratic aide said, with an endless loop of headlines about the president’s signature accomplishment being rejected.