Under increasing pressure from Democrats and members of his own party, Sen. Jim Bunning (R-Ky.) Tuesday night abandoned his one-man filibuster of a one-month extension to unemployment benefits and other programs.

In the end Bunning agreed to a deal allowing him one vote on an amendment to pay for the bill’s $10 billion cost. That proposal was offered by Majority Leader Harry Reid (D-Nev.) and Minority Leader Mitch McConnell (R-Ky.) last Thursday at the start of his filibuster, but Bunning rejected it because he feared his amendment would not pass.

Reid has also agreed to give Bunning two votes on amendments to a larger, one-year extension bill that is currently under consideration in the Senate.

Majority Whip Dick Durbin (D-Ill.) said he was pleased a deal could be reached.

“Bunning is coming back now, he has accepted our offer to have one offsetting amendment, which is an offer we made last week, and now he’s accepted it. I think it’s a new offset, we’re waiting to see. So, we’ll see where it goes,” Durbin said. “So it would give us two votes: offset amendment and final passage of the short-term [unemployment insurance].”

The Senate is expected to vote Tuesday night on the short-term bill, which also includes payments for doctors and highway spending as well as other items.

Thousands of federal highway employees who had been furloughed as a result of Bunning’s filibuster will likely be able to return to work later this week, and unemployment insurance checks will be sent to recipients after several days of delay.

To ensure the deal is enforced, Bunning has placed a hold on all the items included in the nightly “wrap up,” which normally entails a unanimous consent agreement to pass noncontroversial nominations and bills, a GOP aide said. Once the votes have taken place that hold would be lifted, the aide explained.