Despite a White House threat that Obama would veto the legislation, the House approved the measure Thursday 252-172. That was short of the two-thirds margin that would be needed to override a veto.
The 2010 law defines full-time workers who must be offered health coverage as those working at least 30 hours weekly.
The Republican bill would boost that threshold to 40 hours. They say the lower level is putting pressure on companies and forcing many of them to reduce workers' hours to save money.
Democrats say a 40-hour standard would put many more workers at risk.
The Senate hasn't yet considered the legislation.