But there are serious political hangups: By putting forward legislation to make targeted modifications, the health care issue will be propelled back into the national spotlight just as many Democrats are trying to run away from the unpopular law and turn the focus back to economic issues. To get around that, some Democrats say the focus, for now, should be on finding a package of measures that the White House can quickly implement — and go around Congress — a tactic Obama vowed to do repeatedly during his State of the Union address, rather than risk a bitter floor fight in which the outcome is far from assured.

“We’ve reached a point here where the suggestion that a law passed four years ago might be modified to work better is considered politically dangerous,” an exasperated Durbin said. “There are things we can do to make the bill better, and we want to do it.”

Senators said the ideas on how to fix the law span the gamut: how to deal with small businesses that want to grow beyond 50 employees but are worried about providing health coverage; whether to extend the enrollment period for an additional two months beyond March; and whether to allow consumers to keep their cancelled plans for at least two more years; among other issues.

It’s unlikely a single catch-all plan will emerge, but individual senators and small coalitions of Democrats may begin pushing piecemeal proposals if the White House is unable to resolve the problems without the consent of Congress.