WASHINGTON — The struggle in Washington over whether to renew expired jobless benefits for the long-term unemployed is as much about providing aid to 1.3 million out-of-work Americans as it is about drawing the first political line of an election year.

Tuesday’s unexpected vote in the Senate removing one obstacle to a three-month extension of aid attracted the support of six Republicans, illustrating the real-life and political pressures on some GOP lawmakers, including those from states with unemployment above the national average.

Still, the legislation’s outcome is uncertain as Democrats, backed by the White House, and Republicans remain sharply divided over whether the cost of the $6.4 billion program extension should be added to the deficit or paid for with spending cuts. Senate Majority Leader Harry Reid, D-Nev., and White House officials indicated they would be receptive to cuts to offset a yearlong renewal of the program, only if Republicans would first agree to restore the benefits for three months without conditions.

The debate fits neatly into a White House strategy to focus much of this year on longstanding economic disparities and draw Republicans into a midterm fight that Democrats believe they win with the public.