Roby's bill fits in with the broad theme that House Majority Leader Eric Cantor (R-Va.) outlined earlier this year in a speech on "making life work" for people. It would let private sector workers who receive overtime pay take extra time off from work instead of additional salary.
Current law requires that private sector workers who accrue overtime must be paid a wage, although it gives government workers the option of taking time off from work. Roby and other Republicans say the bill would give working families the chance to spend more time together.
However, Democrats have assailed the bill as one that would let companies dodge the requirement of paying overtime wages of 1.5 times regular wages.
"This bill is really about working more and getting less at the end of the week," House Education and the Workforce Committee ranking member George Miller (D-Calif.) said after the committee approved the bill in April.
Republicans have said their bill would only allow companies to pay workers for overtime in the form of time off subject to a voluntary agreement between the employer and the employee.