That has left many Democrats reluctant to ease across-the-board cuts for individual programs that cause a public outcry because they worry that would relieve pressure on Republicans to undo the entire sequester.
"While there is a little bit of leverage and pressure, let's broaden it to the sequester as a whole," Rep. Tim Walz, D-Minn., told reporters before voting against the bill.
Said House Minority Leader Nancy Pelosi, D-Calif.: "How can we sit there and say, 'Four million Meals on Wheels for seniors gone? But that's not important. Over 70,000 children off Head Start. But that's not important.' What is important is for Republicans to hold a hard line" on budget cuts.
Even so, the complaints about flying delays became too intense, and in the end only 29 Democrats and 12 Republicans voted against the measure Friday in the House. The FAA said there had been at least 863 flights delayed on Wednesday attributed to the furloughs, with hundreds of others daily since the furloughs began last Sunday.
The bill would let the FAA use up to $253 million from an airport improvement program and other accounts to halt the furloughs through the Sept. 30 end of the government's fiscal year. The money can be used for other FAA operations, too, including keeping open small airport towers around the country that the agency said it would shut to satisfy the spending cuts.
But Democrats were bitter Friday that cuts in many federal programs remain. Besides the Head Start pre-school program, they complained about ongoing cuts for health research, feeding programs for poor women, children and the elderly and jobless benefits for the long-term unemployed and about furloughs of civilian Pentagon workers.
"Let's get a big deal. Let's deal with all the adverse consequences of the sequester," said No. 2 House Democrat Steny Hoyer, whose Maryland district has many civil servants and who voted no.
Congressional approval was hailed by groups representing the airline industry and the union representing controllers.
"The winners here are the customers who will be spared from lengthy and needless delays," said Nicholas E. Calio, president of Airlines for America, representing major carriers.
The National Air Traffic Controllers Association said the week of problems showed that a "fully staffed air traffic control workforce is necessary for our national airspace system to operate at full capacity."
Associated Press writers Andrew Taylor, Joan Lowy and Nedra Pickler contributed to this report.