WASHINGTON — President Obama and the Republicans in Congress clashed over taxes and wealth on Thursday, a day after many Americans sent checks to the Internal Revenue Service, as the House voted to repeal the federal tax levied on multimillion-dollar estates.

Republican leaders hailed the vote as a victory for farmers and small-business owners who may otherwise be forced to sell assets after the death of a spouse or a parent to pay taxes on property that has already been taxed. The White House called it a giveaway to a few thousand of the nation’s wealthiest families and said it would raise federal deficits.

The vote was the first in a decade to eliminate what Republicans call the death tax, and it stands little chance of making it out of the Senate, much less past the president’s veto pen. But each side saw an opportunity to portray the other as out of touch on an issue that resonates beyond the few who would directly benefit.

“Family farmers, ranchers and small-business owners work tirelessly to create jobs in our communities, put food on our tables and, God willing, have something to pass on to their children and grandchildren,” the House speaker, John A. Boehner, Republican of Ohio, said in a statement. “Taking away that opportunity with a massive death tax bill is simply wrong.”