"Instead of letting the federal government dictate how employers should allocate resources, let's repeal this job-killing mandate and let businesses get back in the business of hiring," Hatch said.
The employer mandate requires that companies of 50 or more workers provide health insurance or pay fines if more than 30 employees receive government assistance to buy coverage.
The health offerings must be affordable, and they must include a variety of "essential health benefits."
Since 2010, several major firms have threatened to cut employee hours over the requirement. Some, like the company that runs Olive Garden and Red Lobster, backtracked after intense criticism.
The Internal Revenue Service has already started to implement the rule in anticipation of next year, when penalties will begin.
Thursday's bill came from Hatch; Senate Health, Education, Labor and Pensions Committee Ranking Member Lamar Alexander (R-Tenn.); and Reps. Charles Boustany (R-La.), Pat Tiberi (R-Ohio) and John Barrow (D-Ga.).