Reps. Todd Young, R-Ind., and Tim Griffin, R-Ark., said President Obama had allowed businesses to delay providing healthcare coverage until 2015, and individuals should be permitted to do the same.
Delivering the GOP's weekly media address, Young and Griffin said Obama had threatened to veto a bill sponsored by them to delay the mandate the House passed Wednesday.
"We take that to mean he thinks it's fair to let businesses off the hook while leaving middle-class families in harm's way," Young said.
The Treasury Department announced early this month it was delaying a mandate that businesses with 50 or more workers provide health insurance, saying businesses needed more time to understand the complex reporting system.
Young said the president should reconsider his threatened veto and called on Democratic Senate leaders "to give our proposals a vote immediately in the name of fairness," ABC Radio News reported, quoting a transcript provided by the Republican Party.
The healthcare law "is a train wreck, plain and simple," Griffin said.
Young added "the sooner we can delay, dismantle, and repeal the president's healthcare law, the sooner we can get people back to work and focus on expanding opportunity for everyone."