"I'm not sure [the revelations] change the political calculus at all for Congress," said Kellie Meiman Hock, a managing partner at McLarty Associates, an international trade consulting firm.
For now, she said, "it is unlikely that the Hill will take any action to limit presidential authority prior to the midterms, even if they disagree with the trade policy."
Trump's "America First" trade agenda was a key to his 2016 victories across the Midwest auto belt, where the flight of factory jobs has left deep scars. But it has alienated many free-trade advocates in his own party and his circle of advisers.
The Woodward book describes how Gary Cohn, the president's former chief economic adviser, quietly scuttled Trump moves to withdraw the U.S. from NAFTA and the trade deal with South Korea.
Representatives from auto states want the president to preserve NAFTA and the regional supply chains it supports, and fear the impact of a trade war on foreign automakers that export from the U.S.
At a Senate hearing last week on auto tariffs, every senator — Republican and Democrat — expressed misgivings about the White House approach on trade, which was variously described as "scattershot," unpredictable, inconsistent and vague.
Labor Committee Chairman Lamar Alexander, R-Tenn., whose state is home to Nissan, Volkswagen and General Motors plants, called the hearing to show how NAFTA benefits Tennessee and urge the U.S. and Europe to eliminate auto tariffs.
Alexander and Sen. Doug Jones, D-Ala., introduced a bill to delay Trump's threatened 25 percent tariff on imported autos and parts until the administration gets a second opinion from the International Trade Commission, an independent agency. The Commerce Department is currently investigating whether such imports are a threat to national security.
"This bipartisan legislation will hold the administration accountable by ensuring it has all of the facts about the positive impact American automakers have on their communities, regardless of where they're headquartered," Jones said in a statement. "With that information in hand, the administration could no longer make the ridiculous claim that this industry is somehow a national security threat."
Jones, whose state is home to Mercedes-Benz, Hyundai and Honda assembly plants, has also joined with two Republicans to promote a measure that would take away the Commerce Department's authority to recommend tariffs on national security grounds and give that power to the Defense Department instead.
This summer, Sen. Bob Corker, R-Tenn., and six House members, led by Rep. Mike Gallagher, R-Wis., proposed that any tariffs tied to national security be subject to congressional approval.
Congress has "authority over tariffs and taxes," John Bozzella, president of the Association of Global Automakers, testified before lawmakers last week. "You should make sure the administration is conducting itself in the way it was intended."