WASHINGTON — At the urging of President Obama, the Democratic and Republican leaders of the Senate set to work Friday night to assemble a last-minute tax deal that could pass both chambers of Congress and avert large tax increases and budget cuts next year, or at least stop the worst of the economic punch from landing beginning Jan. 1.

After weeks of fruitless negotiations between the president and Speaker John A. Boehner, Mr. Obama turned to Senator Harry Reid, the majority leader, and Senator Mitch McConnell of Kentucky, the Republican leader — two men who have been fighting for dominance of the Senate for years — to find a solution. The speaker, once seen as the linchpin for any agreement, essentially ceded final control to the Senate and said the House would act on whatever the Senate could produce.

“The hour for immediate action is here. It is now,” Mr. Obama said in the White House briefing room after an hourlong meeting with the two Senate leaders, Mr. Boehner and Representative Nancy Pelosi, the House Democratic leader. He added, “The American people are not going to have any patience for a politically self-inflicted wound to our economy, not right now.”

Senate Democrats want Mr. McConnell to propose an alternative to Mr. Obama’s final offer and present it to them in time for a compromise bill to reach the Senate floor on Monday and be sent to the House. Absent a bipartisan deal, Mr. Reid said Friday night that he would accede to the president’s request to put to a vote on Monday Mr. Obama’s plan to extend tax cuts for all income below $250,000 a year and to renew expiring unemployment compensation for as many as two million people, essentially daring Republicans to block it and allow taxes to rise for most Americans.