WASHINGTON — Senate Democrats reached an agreement with Republican moderates on Friday to pare a huge economic recovery measure, clearing the way for approval of a package that President Obama said was urgently needed in light of mounting job losses.

The deal, announced on the Senate floor, was a result of two days of tense negotiations and political theater. Mr. Obama dispatched his chief of staff to Capitol Hill to help conclude the talks and reassure senators in his own party, and he called three key Republicans to applaud them for their patriotism.

Earlier, when it looked as if a vote might take place Friday night, officials said, a government plane was dispatched to Florida to bring back Senator Edward M. Kennedy, a Massachusetts Democrat who has brain cancer.

The fine print was not immediately available, and the numbers were shifting. But in essence, the Democratic leadership and two centrist Republicans announced they had struck a deal on about $110 billion in cuts to the roughly $900 billion legislation — a deal expected to provide at least the 60 votes needed to send the bill out of the Senate and into negotiations with the House, which has passed its own version.