Sen. Chuck Grassley Charles (Chuck) Ernest GrassleySenate Republicans signal openness to working with Biden Senators offer disaster tax relief bill Trump spikes political football with return of Big Ten season MORE (R-Iowa) is urging Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellSenate Republicans signal openness to working with Biden Hillicon Valley: DOJ indicts Chinese, Malaysian hackers accused of targeting over 100 organizations | GOP senators raise concerns over Oracle-TikTok deal | QAnon awareness jumps in new poll The Hill's Campaign Report: Biden asks if public can trust vaccine from Trump ahead of Election Day | Oklahoma health officials raised red flags before Trump rally MORE (R-Ky.) to take quick action on the long-awaited U.S.-Mexico-Canada Agreement (USMCA) before an impeachment trial begins in the upper chamber.

Grassley said he is hoping to get the agreement passed in the next several days, before Speaker Nancy Pelosi Nancy PelosiPowell warns failure to reach COVID-19 deal could 'scar and damage' economy Overnight Defense: House to vote on military justice bill spurred by Vanessa Guillén death | Biden courts veterans after Trump's military controversies Intelligence chief says Congress will get some in-person election security briefings MORE (D-Calif.) sends the articles of impeachment to the Senate, which could delay a USMCA vote for weeks.

The Iowa senator said McConnell "wants to do something significant" while the Senate waits for articles of impeachment to come over from the House and that "this would fall into that category."

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However, he warned that if the articles come soon, the Senate will have to move immediately to the impeachment trial.

"The minute those articles come over, that takes precedence under the rules and under the Constitution," he said, noting that the USMCA would then "have to come afterward."

Several Senate committees have jurisdiction over subjects in the trade deal and are currently reviewing it, which could be “a problem” when it comes to quickly pushing the agreement through the upper chamber, the Senate Finance Committee chairman cautioned. The panel voted 25-3 on Tuesday to approve implementing legislation for the deal.

McConnell had said last month that the Senate would not take up the USMCA until an impeachment vote, but that was before Pelosi announced she was withholding the articles.

Nevertheless, John Cornyn John CornynSenate Republicans signal openness to working with Biden Hillicon Valley: DOJ indicts Chinese, Malaysian hackers accused of targeting over 100 organizations | GOP senators raise concerns over Oracle-TikTok deal | QAnon awareness jumps in new poll Republican Senators raise concerns over Oracle-TikTok deal MORE (R-Texas), an adviser to McConnell, indicated that the USMCA was unlikely to pass this week.

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"There are seven committees, so I think they're trying to coordinate that," he said. "I think that's a procedural challenge, and then of course there's a race to the floor. Even if we were to take up the USMCA on the floor, my understanding is that the articles of impeachment would displace it, so it's a bit of a muddle."

Pelosi has not given the House-passed articles of impeachment to the Senate, calling for more details about the proposed rules for the trial. She has not indicated when she will submit the articles.

The House passed articles accusing President Trump Donald John TrumpBarr criticizes DOJ in speech declaring all agency power 'is invested in the attorney general' Military leaders asked about using heat ray on protesters outside White House: report Powell warns failure to reach COVID-19 deal could 'scar and damage' economy MORE of abuse of power and obstruction of Congress last month after a months-long inquiry.

The trade agreement, designed to replace the North American Free Trade Agreement, was also passed in the lower chamber last month after negotiations between the administration and lawmakers, the day after the president was impeached.

Justine Coleman contributed.