But Trump hobbled his team's ability to extract concessions long before these meetings.
First, he withdrew the U.S. from the TPP, which was initiated by President George W. Bush and negotiated by President Barack Obama as a means of linking Pacific nations to create a counterweight to China's power.
More recently, Trump alienated allies such as Canada and the European Union by threatening to apply tariffs on steel and aluminum to them as well as China. That creates double-barreled problems for U.S. business.
With Trump this week deferring decisions on the scope of tariffs, and the EU and China threatening retaliation, uncertainty hangs over business purchasing and investment decisions.
China has already imposed new tariffs on American sorghum, a blow to farmers in Kansas, and threatened similar steps against soybeans and other agricultural products that would hit Trump-friendly voters elsewhere in the Midwest.
Whatever the administration decides, recent history points toward net negative economic efforts. Analyses of steel tariffs imposed by Bush found they created fewer jobs in steel production than they destroyed through higher prices for steel-consuming industries.
The Trump administration wields the possibility of tariffs on Canada and Mexico as leverage to achieve U.S. goals in a renegotiated NAFTA. As the president warns of scrapping the existing deal, representatives of all sides report rising prospects that they'll reach a new one.
The good economic news from such a deal is that it would modernize an agreement struck before the digital revolution turned commerce upside down. The bad news? Modernization had been agreed upon before Trump took office as part of TPP, and now it may come with new provisions counterproductive for U.S. business overall.
"Trump created a crisis for NAFTA in order to appeal to his protectionist constituencies," said Robert Zoellick, Bush's U.S. trade representative. "The priorities of his rewrite, if Canada and Mexico agree, are supposed to restrict North American trade and investment, not boost our competitiveness with the world."
One priority is changing "rules of origin" to require that a higher proportion of North American cars be produced within the U.S. Zoellick said that objective comes with rules on inputs and wage rates "that would appeal to a central planner from the old days."
That worries the auto and auto parts industries, along with the lawmakers who speak for them in Congress. Record-keeping requirements and disruption to existing supply chains, they warn, could outweigh the benefits of avoiding U.S. tariffs and lead manufacturers to shift production elsewhere and increase reliance on automation.
The administration also wants a "sunset" allowing the U.S. to exit a new NAFTA after five years. While that appeals to a president who built a reality television career around the words "you're fired," it undercuts the predictability corporations need for long-term planning.
"The climate it creates stops investment," said Carla Hills, trade representative under President George H.W. Bush. "We look like we no longer have reliability."
Trump's strategy for pursuing a new NAFTA adds another danger. The administration has discussed scuttling the existing agreement at the same time it submits a new one to Congress.
The idea would be pressuring reluctant lawmakers to vote yes. But that poses the risk of calamitous economic disruption if a White House with limited success on Capitol Hill fails to gather and accurately count the necessary votes.
Achieving a new NAFTA would still leave the administration with lost economic ground to make up. By scuttling TPP, Trump sacrificed market-opening steps for U.S. businesses in Japan and Vietnam, among other countries.
As a result, the president has suggested the possibility of shifting course and belatedly joining TPP. Hills, a Cabinet member in two Republican administrations, hopes the administration can at least pull off a modernized NAFTA.
But, she said, "we've got a lot to worry about."
Correction: An earlier version misstated the length of a "sunset" clause that would allow the U.S. to exit a new NAFTA. It's five years.