Sens. David VitterDavid Bruce VitterRed-state governor races put both parties on edge Louisiana Republicans score big legislative wins Trump calls on Republicans to vote out Democratic Louisiana governor amid GOP infighting MORE (R-La.) and Jeff SessionsJefferson (Jeff) Beauregard SessionsTrump attends football game with Jeff Sessions' Alabama Senate race opponent Bradley Byrne Impeachment tests Barr-Trump relationship Tide, Tigers and Trump: President hopes for home-field advantage in Alabama MORE (R-Ala.) asked that the legislation, the Child Tax Credit Integrity Preservation Act (S. 577), be moved onto the floor for a vote.

The legislation aims to block illegal immigrants from receiving a child tax credit.

"The reality is because of this enforcement problem, because of this loophole in terms of how the child tax credit is enforced, illegal aliens who pay no taxes, who are not entitled to this benefit, to this check from the government, receive $4.2 billion alone," Vitter said. 

"The fix is simple and it's clear, the IRS and the Treasury Department has told us. We simply need to mandate that folks applying for the credit use valid social security numbers. That will cut off the fraud, that will cut off $4.2 billion going improperly to illegal alien families. It will not cut off the benefit going to anyone who deserves it under the law."

In response, Senate Majority Leader Harry ReidHarry Mason ReidLobbying world Democrats aim to protect Grand Canyon from 'imminent' drilling threat Warren's careful approach with media pays off MORE (D-Nev.) objected to the consent request. He said that the tax code already outlaws the kind of tax fraud Vitter and Sessions were trying to discourage with the legislation.

"Seems to me the problem is illegal aliens receiving the credit wherever they are physically, not people outside the country receive the credit —some of whom would qualify for the credit," Reid said.

"The Vitter-Sessions legislation, however, eliminates the tax credit for filers who are compiling with the law," Reid continued. "That isn't a good result. In fact, this legislation that's proposed here fails to address the issue of the child tax credit being claimed for children not living in the United States. So the problem is not being solved by this legislation. The legislation goes well beyond what's necessary to stop fraud and the child tax credit program."

Reid added that it was important that any children who are in the United States legally receive the benefits. In response, Vitter said they he and the majority leader had the same goal in mind.

"We have the same goal in mind exactly, and I believe this approach of the Vitter bill —the House has already passed this approach recently in its budget outline, actually accomplishes that because by requiring a valid social security number we allow everyone who truly qualifies for the credit to get it and we stop it from going to illegal alien families who do not deserve the credit under the law," Vitter said.

The House approved language in its Sequester Replacement Reconciliation Act meant to do the same thing as the Sessions-Vitter bill. Sessions said that because the House had already passed similar legislation, the Senate bill could become law soon.

"If we pass it, it will become law in a matter of days perhaps," Sessions said.