The vote was 97 to 318, with seven Democrats voting "present." Two-thirds support was needed for the measure to pass.
"Americans across the country recognize that this wild spending spree the president's been on the last two years has to come to an end, and it's going to start here on the House floor where we're finally going to invoke fiscal discipline," Rep. Steve Scalise (R-La.) said during a floor debate Tuesday.
Critics say the GOP is playing with fire as it complicates an issue being watched by financial markets worldwide. Democrats, many of whom joined Republicans in voting against the measure, called it "a political stunt."
"This is about threatening to default on the full faith and credit of the United States unless we put in to place the Republican budget, including their plan to end the Medicare guarantee and to slash Medicare benefits," said Rep. Chris Van Hollen (D-Md.), the ranking Democrat on the House Budget Committee.
The White House on Tuesday issued a fresh call for Congress to pass a higher debt limit. At his daily briefing, White House Press Secretary Jay Carney read from a letter that Ronald Reagan sent in 1983 to the then-Senate Republican leader, warning that "the full consequences of a default, or even the serious prospect of default by the United States, are impossible to predict and awesome to contemplate."
Congressional leaders and the Obama administration are now in weekly meetings to reach an agreement on budget reforms before the Aug. 2 deadline to avoid a federal default.
"We are committed to reducing the deficit. That's why we have moved so aggressively and seriously with these negotiations, why we're encouraged by the fact that they have produced positive results so far," Carney said.
Asked whether the vote was a "useful exercise," Carney replied succinctly, "It's fine."
Obama will meet with House Republican and Democratic caucuses separately this week. Vice President Joe Biden, who has been the White House point person for fiscal talks, is on a trip to Italy this week.