Two brave Democrats voted for President Obama’s budget on Wednesday, preventing another unanimous defeat for their party leader.

The rest of the chamber, however, had other plans, sending Mr. Obama’s plan to a devastating 413-2 defeat as most Democrats joined Republicans in rejecting the fiscal year 2015 blueprint.

House Republicans staged the vote to be able to argue that Mr. Obama’s plans are unpopular on both sides of the aisle, though Democrats said it was a useless vote and said the plan — which Republicans wrote to reflect the president’s budget — wasn’t actually Mr. Obama’s own plan.

The GOP staged similar votes in 2012, and Mr. Obama’s plan was unanimously defeated in both the House and Senate that year. Last year, Mr. Obama submitted his budget months later than the deadline, which meant the House didn’t even have his plan in time for its own vote.