The measure now goes to the Senate where Majority Leader Harry Reid, D-Nev., said action on the bill would be taken immediately.
The White House said President Obama would sign the measure even though he would prefer a long-term deal.
The suspension through May 19, which passed 285-144, is conditional on the U.S. Senate passing a budget resolution by mid-April.
"Today I'm pleased that Speaker [John] Boehner's House colleagues have decided to change course and pass a bill that diffuses yet another fight over the debt ceiling," Reid told reporters. Reid, however, called the budget requirement a meaningless gimmick, The Hill reported.
The United States reached its $16.4 trillion borrowing limit New Year's Eve.
The bill would let the U.S. Treasury keep borrowing money to pay its bills but would not require lawmakers to vote on actually raising the debt ceiling.
Once the suspension period ends, the borrowing limit would be adjusted upward to account for the country's increased debt level.
"The bill still has to overcome some concerns expressed by members of the House and the Senate before it can pass both chambers and reach the president's desk," White House spokesman Jay Carney said Tuesday.
"If it does [pass Congress] and it reaches the president's desk, he would not stand in the way of the bill becoming law.
"Clearly, we support extension of the debt ceiling without drama or delay. That has been his position forever -- as president and since we've had these rather novel debates about whether or not we should engage in games of chicken over the full faith and credit of the United States."
The White House later said Obama looked forward "to continuing to work with both the House and the Senate to increase certainty and stability for the economy."