The Justice for Victims of Trafficking Act, introduced by Sen. John Cornyn (R-Texas), includes additional resources for law enforcement. It also establishes a fund to raise money for victims.
McConnell called the legislation a byproduct of multiple committees and bipartisan cooperation.
"Senators from both sides of the aisle and from multiple committees have worked hard to address the terrible crime of human trafficking," the Kentucky Republican said from the Senate floor. "Victims groups and advocates have called this bipartisan measure the most comprehensive and thoughtful piece of anti-trafficking legislation currently pending."
McConnell said on Monday afternoon that senators will debate the bill from 11 a.m. to 12:30 p.m. on Tuesday. The Senate could also take up amendments to the bill on Tuesday afternoon after party lunches.
Reid suggested the bill could bypass some of the procedural hurdles that normally slows legislation.
"I think it would be a waste of the Senate's time to have a motion on a vote to proceed and a waste of time afterwards," he said. "So I hope that we can get on this legislation tomorrow. I doubt if there will be problems on my side. If there is, I will work to clear them."
Sen. Patrick Leahy (D-Vt.) suggested earlier this month that that he would try to bring up his Runaway and Homeless Youth and Trafficking Prevention Act, which aims to prevent youths from being trafficked, when senators take up Cornyn's bill.
McConnell, however, said that he hopes that after time for amendments and debate the legislation sees "strong bipartisan support here on the Senate floor."