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.