McConnell followed by filing cloture on a Republican plan, S. 1726, that would "repeal the onerous three-percent withholding provision," an issue that is also included in President Obama's original "jobs" legislation. 

The rule the GOP plan looks to repeal mandates that federal, state, and local governments withhold three-percent of many of  their contract payments, Medicare payments, farm payments, and some grants. 

"The bill is an example of the type of jobs legislation that Sen. McConnell has long said the Senate should consider: it’s a measure with bipartisan, bicameral support that the president will sign," said a statement from the minority leader's office issued late Wednesday evening. 

Republicans have already pledged to oppose Reid's plan, characterizing it as another federal "bailout" for struggling states and local governments. McConnell's plan, however, could put some Democrats in a tight spot since President Obama has previously suppoted its provision.

The timing of the two votes is yet to be scheduled.