The House signed off on Trump's trade deal in December after months of closed-door haggling between House Speaker Nancy Pelosi (D-Calif.) and the Trump administration.

McConnell had initially indicated that the trade deal would have to wait until after the impeachment trial wraps next month.

But the standoff between McConnell and Pelosi delayed the articles, and therefore the start of the Senate trial, giving senators an opening to approve the trade deal before impeachment gets underway.

Sen. John Thune (S.D.), the No. 2 Republican senator, told reporters on Tuesday that Republicans were hoping to get the USMCA through the chamber this week, though he stressed it would depend on cooperation on the Senate floor.

Sen. Lisa Murkowski (R-Alaska) told reporters that she had also been told from GOP leadership that they would try to get the trade deal done this week.

"It sounds like it," she said. "I think all the committees that have a piece of the jurisdiction are all disposing of it."