The Senate's top Republican said Tuesday that a vote on President Donald Trump's NAFTA replacement won't come until 2019, potentially setting up a showdown with Democrats if, as expected, they win a majority in the House.

"That'll be a next year issue," Senate Majority Leader Mitch McConnell, R-Ky., told Bloomberg News, citing procedural issues. "There's no question this will be on the top of the agenda."

Indeed, the legislative calendar for the rest of the year is tight. Lawmakers are campaigning for re-election ahead of next month's midterm election. Several other pressing issues await senators when they get back for the lame-duck session after the election, such as the farm bill and another deadline to fund the government.

The U.S., Mexico and Canada reached an 11th-hour deal late last month to keep much of the old North American Free Trade Agreement alive, with a few distinct changes. The updated pact, which is now called the USMCA, still needs to be approved by each nation's legislatures.

Some Republicans had been pushing for a vote on the deal this year, but it was always unlikely given the remaining priorities for this congressional term.

Democrats have been largely supportive of keeping NAFTA in place. Yet, if the party takes power in the House, its members could push for concessions and complicate the approval process. The GOP, meanwhile, is expected to hold onto or expand its slight majority in the Senate.

Key Republicans have also suggested that the refreshed trade agreement needs improvement. Sen. Pat Toomey, R-Pa., told CNBC earlier this month "there's a possibility that we could address some of these what I consider flaws in the implementing legislation that Congress has to pass."

Even though the USMCA isn't officially in place, that hasn't stopped Trump from touting it on the campaign trail, particularly as he seeks to limit the political damage wrought by his tariffs and trade conflict with China and other nations.

"NAFTA has been one of the great disasters of all time and now we have a great and fair deal. We have a fair deal," the president said at a rally earlier this month in Minnesota.

Read the full Bloomberg News story here.