WASHINGTON—The House on Thursday approved an extra three months of jobless benefits for all unemployed Americans, knowing the plan’s chances are slight in the Senate and almost nonexistent at the White House.

After failing to get a veto-proof two-thirds margin by three votes on Wednesday, Democrats got an exact two-thirds margin on Thursday with a 274-137 vote—the amount needed to overcome a threatened presidential veto.

Democrats said they pushed the legislation through to the Senate because Americans need help in a slumping economy.

The Labor Department reported Thursday that the number of people filing new claims for unemployment benefits last week increased by 25,000 from the week before. The unemployment rate in May jumped to 5.5 percent, up from 5 percent in April. It was the biggest one-month gain in 22 years.

“The American people are waiting to see if Congress is going to help them,” said House Speaker Nancy Pelosi, D-Calif.

But the White House already has threatened to veto the bill, and Senate Democrats have said they won’t try and force their Republican colleagues to consider the House legislation.

Senate Majority Leader Harry Reid, D-Nev., said he will try to bring up the House bill, but he won’t force the issue if Senate Republicans object. “We’re not wasting weeks” on it, he said. Instead, Reid said, Democrats might attach the jobless benefits extension to the Iraq war spending bill, a move also opposed by the White House.

The White House and Republicans said a bill targeting unemployment benefits only to states that have high unemployment would be more palatable to them. The Democrats’ plan “is dead on arrival,” House Republican leader John Boehner of Ohio said. “The Senate’s not going to take it up.”

The House legislation would extend unemployment benefits for an additional 13 weeks in all 50 states and the District of Columbia for workers who exhaust their regular 26 weeks of unemployment benefits.

States with an unemployment rate of 6 percent or more would get an additional 13 weeks of unemployment benefits. Michigan (6.9 percent), Alaska (6.7 percent), California (6.2 percent), Rhode Island (6.1 percent) and the District of Columbia (6.0 percent) are the only places that qualify currently. The extension would run through March, although unemployed workers who are already getting extra benefits before then would get their entire 13 weeks.

The Congressional Budget Office estimated that about 3.2 million Americans would collect $11.7 billion in extended unemployment benefits over the life of the extension.