WASHINGTON — The Senate on Monday agreed to extend the federal unemployment insurance program to about 2.8 million people nationwide who have lost jobs and exhausted their state benefits, but haven’t found new work.The bill passed 59-38, but its future remains uncertain. The Republican-controlled House has criticized the bill, and party leaders have not indicated whether they will allow a vote.Democrats see the jobless benefits issue as a help in the midterm elections, particularly in the Senate, where control of the chamber could hang in the balance. The more Republicans resist, the more Democrats intend to portray them as insensitive to the needs of unemployed Americans who have not benefited from the end of the recession.Republicans often counter that as long as people can collect benefits, they’ll rely on government money and not have incentive to look for work. And, Republicans often argue, the best way to ease unemployment is to provide other incentives for job creation.Michael Steel, a spokesman for House Speaker John Boehner, said Monday that Boehner for months has said House Republicans would consider extending emergency unemployment insurance if it included provisions that would create more private-sector jobs.The Senate bill makes the extension fully paid for with a combination of offsets, including “pension smoothing,” an accounting maneuver that allows companies to pay less into their pension funds temporarily, which raises their taxable income.“We have bent over backwards to pass a strong bipartisan unemployment insurance bill that incorporates Republican ideas,” said Sen. Charles Schumer, D-N.Y., chairman of the Senate Democratic Policy Committee. There is some sentiment to make the five-month extension start now and continue through early next fall, instead of being retroactive. Last Friday, House Majority Leader Eric Cantor, R-Va., would not rule that out when asked about it on the House floor by Minority Whip Steny Hoyer, D-Md.Doing so would resolve one issue Republicans often mention: They have maintained retroactivity would be an administrative nightmare. It also would push any talk of another extension into the general election season.Both parties regard the issue as important for firing up their bases, which can be important in midterm elections where turnout can be crucial.