An aide to Mr. Schumer said that no invitation has been offered.
Last week, Mr. Trump even embraced Senator Bernie Sanders of Vermont on trade. The president said that Mr. Sanders, who is making his second presidential run as a Democrat, tends to agree with him on the issue and that Mr. Sanders is “tough on trade.”
While Mr. Sanders has praised some of Mr. Trump’s moves on trade, he has also been critical of his negotiating approach in some cases, and has opposed the Trump administration’s steel and aluminum tariffs on Canada, Mexico and Europe.
Mr. Pillsbury said that Mr. Trump’s campaign advisers have been gathering opposition research files on potential 2020 rivals and carefully taking note of what certain people, such as Senator Sherrod Brown, the Ohio Democrat who is considering a run, have been saying about China.
Mr. Brown was one of three top Democrats — along with Mr. Schumer and Mr. Wyden — who sent a letter to Steven Mnuchin, the Treasury secretary, this month urging the administration to “stay aggressive” and ensure that China commits to verifiable, enforceable reforms. The letter was sent following reports that Mr. Mnuchin wanted to scale back Chinese tariffs in advance of a deal.
“I will wait to judge the outcome of the trade talks until I know what’s been agreed to,” Mr. Brown said in a statement. “But it’s imperative that the White House secures an enforceable deal that includes long-term structural reforms to stop China’s unfair trade practices and ensures American workers can compete on a level playing field.”
Officials from both countries have continued to be vague about the details of the progress, leading to speculation that China is just repackaging old promises as new concessions. China experts and business lobbyists say that the Chinese government has been carefully watching the shifting political dynamics in the United States, along with Mr. Trump’s ongoing legal turmoil, as it determines how to navigate the trade war in an environment with Democrats controlling more power in Washington.
In some cases, newly empowered Democrats have become an asset to the administration’s China hawks, Mr. Lighthizer and Peter Navarro, who have been pressing Mr. Trump not to cut a modest deal and roll back tariffs to please Wall Street.