And Senator Susan Collins of Maine, a moderate Republican colleague of the conservative Mr. Bunning, joined Democrats in trying to force the measure through, calculating that perhaps a plea from a fellow Republican would get him to change his position.

“When I was home this weekend, I talked to constituents who expressed their utter bafflement that Congress could not proceed on something that has widespread support,” Ms. Collins said.

“While trying to blame Democrats for mishandling the entire matter, other Republicans also distanced themselves from Mr. Bunning, whom Democrats were holding up as the embodiment of what they say has been a maddening pattern of Republican obstruction in the Senate.

“This is one senator,” said Senator John Cornyn of Texas, a chief political strategist for Senate Republicans. “This does not represent the position of the caucus.”

Other party officials said that while the Bunning fight was not helpful, it probably would not do serious damage as long as it ended rapidly.

Republicans were not just unhappy that the back-and-forth was allowing Democrats and editorial writers around the country to portray them as heartless curmudgeons, denying jobless aid to struggling Americans while Mr. Bunning complained that late-night debate was preventing him from watching a college basketball game.

The attention to the impasse was also cutting into Republican efforts to focus on the evolving Democratic strategy on the health care overhaul, which Republicans are trying to portray as an end-run around Senate rules. Instead, Democrats were having a field day citing Mr. Bunning’s repeated objections as evidence of how Republicans abuse the rules to delay needed legislation, helping them build a case in favor of using any available tools to overcome such opposition.