The measure still needs approval in the Senate, where Democratic Majority Leader Harry Reid said it will be rejected.
"To be absolutely clear, the Senate will reject both the one-year delay of the Affordable Care Act and the repeal of the medical device tax," Reid said.
The House vote brings the federal government dramatically closer to its first shutdown in 17 years.
Barely two days before a shutdown deadline, Republican leaders set off a political firestorm when they announced yesterday that their stopgap federal spending bill aims to delay implementation of so-called Obamacare by one year.
More From This Section
It also vowed to veto any such bill. Both chambers would need a two-third majority vote to override a presidential veto, which is close to impossible given the current political breakdown on Capitol Hill.
House Speaker John Boehner nevertheless ploughed ahead with the strategy, convening a rare Saturday session as Congress struggled to break a funding impasse that, if unresolved, would require hundreds of thousands of federal workers to stay home.
After hours of raucous debate, the House approved the measure, voting largely along party lines.
Under pressure from his party's far-right conservative wing, Boehner doubled down on his caucus's bid to stop Obama's signature domestic achievement, the health care law.
The Senate had already stripped a House spending bill of a provision fully defunding Obamacare and sent it back hoping the lower chamber would sign off on it.