Democrats, who have been dismissed as obstructionists by Republicans determined to repeal and replace the law without them, are sitting by quietly waiting for those efforts to fail. At that point, Democrats believe, Republicans will have to reach across the aisle and repair the law.

“We’ve maintained all along there is room to negotiate,” said Senator Brian Schatz, Democrat of Hawaii. “But only if they abandon their attempt to repeal the law.”

While he has seen no moves toward cooperation yet, “they are in a world of hurt,” Mr. Schatz said of Republicans, “because none of their plans add up, and their members are starting to figure this out and the public is starting to figure this out, and they don’t have Obama as a foil anymore. I think they need to fail first.”

Senator Claire McCaskill, Democrat of Missouri, who has long offered to help fix the law, said she had heard from only one Republican colleague, Senator Bob Corker of Tennessee, since the end of last year. “I don’t think Republicans have decided what they’re waiting for,” she said. “The White House or Godot.”

Many Republicans seem to be resigned to seeking consensus on health care legislation, as well as on a budget and tax reform, without comprehensive White House guidance.