U.S. Trade Representative Robert Lighthizer Robert (Bob) Emmet LighthizerWhiskey, workers and friends caught in the trade dispute crossfire GOP senator warns quick vote on new NAFTA would be 'huge mistake' Pelosi casts doubt on USMCA deal in 2019 MORE faced pushback and a “bucket full” of questions Thursday during a closed-door caucus lunch meeting meant to sell Senate Republicans on the new trade deal with Canada and Mexico.

Republican senators stressed that they expect the U.S.-Mexico-Canada Agreement (USMCA) will have the votes to pass the Senate, but acknowledged there was still opposition within the caucus and broader frustration with how the trade negotiations had been handled.

“There’s some opposition to some pieces of it, as you might imagine,” Sen. David Perdue (R-Ga.) told reporters after the lunch.

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Perdue added that “personally, I would have liked to have a little more time to look at it,” but predicted that the trade deal wouldn’t lose a lot of Republican votes when it comes to the floor next year.

Sen. Roy Blunt Roy Dean BluntSunday shows preview: Lawmakers prepare for SCOTUS confirmation hearings before election SCOTUS confirmation in the last month of a close election? Ugly Senate to push funding bill vote up against shutdown deadline MORE (Mo.), a member of GOP leadership, acknowledged that Lighthizer got some criticism from Senate Republicans but stressed that it was “not a lot.”

“I think you could summarize the ambassadors presentation as: This is a big improvement over NAFTA. But it’s not quite as good as the bill he originally negotiated, but he is still thinks it's a big improvement,” Blunt said, in reference to the North American Free Trade Agreement. “The questions were ... mostly about the things that had changed."

House Democrats announced earlier this week that they had reached a deal with the White House on USMCA after months of closed-door negotiations on the updated version of the North American Free Trade Agreement.

The announcement of the deal, and the fact that they had brought labor on board, prompted skepticism among Republicans who worried the agreement had shifted too far to the left.

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“It’s imperfect, and some people are concerned about the more recent negotiations,” said Sen. Kevin Cramer Kevin John CramerNetflix distances from author's comments about Muslim Uyghurs but defends project Abortion stirs GOP tensions in Supreme Court fight Momentum growing among Republicans for Supreme Court vote before Election Day MORE (R-N.D.), but added that he thought a “vast majority” were comfortable with the agreement.

Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellHawley warns Schumer to steer clear of Catholic-based criticisms of Barrett Senate GOP set to vote on Trump's Supreme Court pick before election Harris slams Trump's Supreme Court pick as an attempt to 'destroy the Affordable Care Act' MORE (R-Ky.) has said the Senate will not take up the trade deal until next year after the chamber finishes an expected impeachment trial for President Trump Donald John TrumpBiden says voters should choose who nominates Supreme Court justice Trump, Biden will not shake hands at first debate due to COVID-19 Pelosi: Trump Supreme Court pick 'threatens' Affordable Care Act MORE.

“From my perspective, it’s not as good as I had hoped," McConnell told reporters during a weekly press conference Tuesday.

But GOP senators indicated after the Lighthizer meeting that there are concerns about the process for how the trade deal will move through the Senate.

Sen. John Cornyn John CornynSupreme Court fight pushes Senate toward brink Hillicon Valley: Productivity, fatigue, cybersecurity emerge as top concerns amid pandemic | Facebook critics launch alternative oversight board | Google to temporarily bar election ads after polls close Lawmakers introduce legislation to boost cybersecurity of local governments, small businesses MORE (R-Texas), a top adviser to McConnell, said he did not expect the Senate Finance Committee to have a mock markup of the trade deal, which under previous agreements would allow them to suggest changes that could be worked in to a final proposal.

“It’s a bad practice and I don’t think the Senate should just quietly agree to be jammed in the process,” Cornyn said, adding that it was a “lousy way to treat the Senate.”

Sen. Pat Toomey Patrick (Pat) Joseph ToomeyAppeals court rules NSA's bulk phone data collection illegal Dunford withdraws from consideration to chair coronavirus oversight panel GOP senators push for quick, partial reopening of economy MORE (R-Pa.) said he had also heard the Senate Finance Committee would not be holding a mock markup of the trade deal.

“We have to have an opportunity to weigh in on that,” Toomey said. “This is a problem.”

Toomey said he raised his concerns with Lighthizer during the lunch and at two separate meetings with Senate Finance Republicans.

When asked if he spoke directly to Lighthizer about his concerns, Toomey said: "I did. In fact, I raised them at the meeting we had before the lunch and I raised them on the phone call the day before that."