WASHINGTON — The Senate failed to move forward on a three-month extension of assistance for the long-term unemployed on Thursday, leaving it unlikely that Congress would approve the measure soon while undercutting a key aspect of President Obama’s economic recovery plan.

Fifty-nine senators, including four Republicans, voted to advance the legislation, falling one vote short of the 60 needed to break a Republican filibuster effort.

Republicans and Democrats, many from the nation’s most economically depressed states, had been trying to reach a solution that would allow people who have exhausted their unemployment insurance to continue receiving benefits as long as the government offset the $6 billion cost.

Ultimately, how to pay for the program proved too big a hurdle for senators to overcome.

“We’ve given them everything they wanted. Paid for,” said Senator Harry Reid of Nevada, the majority leader, flashing his irritation at Republicans who blocked the bill.