Democrats and union leaders have argued that the NLRB is an important tool in maintaining worker's rights and keeping jobs in the United States. But Republicans believe that the board is an example of government overreach and unnecessary regulation.

For his part, Scott is hoping that his bill will get a vote on the Senate floor. Although prospects are dim in the Democrat-controlled Senate, Sen. Lindsey GrahamLindsey Olin GrahamTrump upends controversial surveillance fight The Hill's Morning Report - Presented by Facebook - Trump on US coronavirus risks: 'We're very, very ready for this' Surveillance fight emerges as intelligence flashpoint MORE (R-S.C.) has promised to fight for a floor vote on the legislation.

"If it does [get to the floor], I believe there will be enough senators on the Democratic side for this bill because it is really not an anti-union bill, it is an anti-federal government overreach bill," Scott said. "We have an opportunity to continue to work toward a legislative solution to the problem created by the regulatory environment."

But Scott acknowledged that the odds of legislative success were still long, and that the dispute was likely headed toward an arbitration or out-of-court settlement.

"Unfortunately, that means some back-room deal that does not work in favor of employees," Scott said.