The Senate tried to pass the Cybersecurity Act of 2012 this summer, but several Republicans pulled support for the bill after the U.S. Chamber of Commerce complained that it put too many requirements on the private sector. Since then, Sens. Joe Lieberman (I-Conn.) and Susan CollinsSusan Margaret CollinsOvernight Energy: Dems raise new questions about Pruitt's security | EPA rules burning wood is carbon neutral | Fourth GOP lawmaker calls for Pruitt's ouster | Court blocks delay to car efficiency fines How much does the FDA really do to promote public health? Trump aide: Mueller probe 'has gone well beyond' initial scope MORE (R-Maine) have been working with Republicans who opposed the measure, such as Sens. John McCainJohn Sidney McCainManchin, Donnelly back Pompeo This week: Senate barrels toward showdown over Pompeo Romney forced into GOP primary for Utah Senate nomination MORE (R-Ariz.) and Kay Bailey Hutchison (R-Texas), to resolve some issues.

On Tuesday, the Senate approved a motion to proceed to the Sportsmen’s Act, S. 3525, which would increase access to federal land for hunters and fishermen while also supporting conservation measures. Amendments to that bill are due by 4 p.m.

Reid also said he was optimistic that Republicans and Democrats would agree to a list of amendments to advance a vote on the sportsmen's bill by the end of Wednesday, rather than Thursday. 

Reid said he hopes to have an agreement on both bills "in the next couple hours."

A Senate aide said if a deal is reached, a vote on the cybersecurity bill could happen as early as Wednesday.

Reid voted against the bill as a procedural move in August so he could bring it back to the floor at a later time. Because of this, the Senate aide added that Reid can bring up the cybersecurity bill at any time as a motion to reconsider that vote.

The next bill the Senate will take up is the Defense Authorization Act, S. 3254.

Jennifer Martinez contributed.