After the standoff was resolved -- following bipartisan pressure from Bunning's Senate colleagues -- the Senate voted in favor of the measure, which extends unemployment benefits, highway funds and other federal programs for 30 days, The Washington Post reported. Bunning had been holding up Senate action on the measure, arguing the bill should be paid for and not financed through deficit spending.
Sen. Susan Collins, R-Maine, joined Democrats in urging Bunning to relent, The New York Times reported.
"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," she said.
NBC News said the agreement allows Bunning to offer his own proposal on how the bill should be paid for.
Bunning, 78, who isn't seeking re-election, wended his way through reporters and cameras to a senators-only area, saying he would continue to block the bill "until it was settled" and a possible solution was being developed.
"One single Republican senator is standing in the way of unemployment benefits for 400,000 Americans," Sen. Patty Murray, D-Wash., said on the Senate floor. She said Bunning's stand also blocks COBRA health insurance benefits and forced doctors to take a 21 percent cut on Medicare reimbursement rates.
Hundreds of thousands of jobless Americans lost their jobless benefits Monday, and the federal government furloughed about 2,000 employees without pay because of Bunning's efforts, the Post said.
Some senators supported Bunning's tactic, the Times said.
"Jim Bunning is my hero," Sen. Jim DeMint, R-S.C., said.
White House spokesman Robert Gibbs said Bunning's action was "irrational."
"I don't know how you negotiate with the irrational," Gibbs said. "I don't know how you prevent one person who decides they hold in the palm of their hand the livelihood of hundreds of thousands who have lost their jobs."
Senate Majority Leader Harry Reid, D-Nev., said Bunning's "point has been made."