President Trump’s top trade official briefed Senate Republicans on the new trade agreement with Canada and Mexico on Thursday — an attempt to soothe tensions with GOP senators who have voiced frustration that the administration conceded too much to House Democrats to win their support for the deal.

Robert E. Lighthizer, the U.S. trade representative, met with all GOP senators at a lunch to detail key changes to the U.S.-Mexico-Canada trade agreement. He also separately briefed Republican and Democratic members of the Senate Finance Committee, which oversees trade policy, earlier Thursday.

Both the White House and congressional Democrats have touted the rewrite of the existing North American Free Trade Agreement as a vast improvement over the original 1990s-era compact. But many Republicans have been skeptical about the enthusiastic support for the new trade deal from Democrats and labor unions, and questioned whether the agreement moved too far to the left at the expense of GOP trade priorities.

Some Republicans — including Sen. Patrick J. Toomey (Pa.), probably the most vocal GOP critic of the administration’s NAFTA rewrite — have criticized the substance of the administration’s accord with House Democrats. But most of the annoyance among Republicans has centered largely on their sense that the GOP was cut out of the administration’s negotiations with House Speaker Nancy Pelosi (D-Calif.) and her ranks.

Sen. John Cornyn (R-Tex.) told reporters that he registered process complaints with Lighthizer and that the administration had jammed the Senate in negotiating directly with Democrats. That, Cornyn said, was a “lousy way to treat the Senate.”

“I’ve supported NAFTA, and I support this,” Cornyn said. “But I don’t appreciate the Senate being ignored as part of the process.”

Despite the GOP complaints, Congress is still likely to support the trade agreement with large margins, with Senate Majority Whip John Thune (R-S.D.), the party’s chief vote counter, conceding that “everybody kind of realized, too, that it’s a take-it-or-leave-it proposition.”

Still, that didn’t stop the venting in private.

During the lunch with Senate Republicans and Lighthizer, Sen. Ted Cruz (R-Tex.) told the trade official that the administration conceded too much in the negotiations to demands from congressional Democrats, according to an official in the room who spoke on the condition of anonymity to disclose a private conversation.

Cruz has previously expressed concerns about a provision in the trade deal that he has characterized as a “grant of immunity to Big Tech” — language that shields tech companies from lawsuits for content people post on their websites.

“I’m disappointed to learn that Section 230 language is still in the trade deal — especially when lawmakers across the political spectrum express serious concerns,” Cruz said earlier this week.

Tying Senate Republicans’ hands further is the fast-track procedure that is being deployed to pass the trade deal with Canada and Mexico in Congress — which significantly limits the ability of lawmakers to amend the substance of the agreement.

“Everybody knows that at the end, it’s pretty much an up-or-down-type option,” Thune said. Lighthizer, he continued, “walked through some of the changes they made on labor provisions and enforcement and some of the environmental stuff.”

Thune added: “But like I said, at this point, kind of academic. You either take it or leave it.”

The House is expected to ratify the trade agreement before the end of the year.

Senate Majority Leader Mitch McConnell (R-Ky.) has said that senators won’t vote on it until after the impeachment trial of Trump, which will almost certainly begin in early January.

“It’s imperfect,” Sen. Kevin Cramer (R-N.D.) said. “And some people are concerned about the more recent negotiations. But at the end of the day, the speaker of the House and her majority have a lot to say about it, and I think the vast majority of us feel comfortable [Lighthizer] got the best deal he could get.”