Sheinbaum said she was willing to engage in talks on the issues, but said drugs were a U.S. problem.
"One tariff would be followed by another in response, and so on until we put at risk common businesses," Sheinbaum said, referring to U.S. automakers that have plants on both sides of the border.
She said Tuesday that Mexico had done a lot to stem the flow of migrants, noting "caravans of migrants no longer reach the border." However, Mexico's efforts to fight drugs like the deadly synthetic opioid fentanyl — which is manufactured by Mexican cartels using chemicals imported from China — have weakened in the last year.
Sheinbaum said Mexico suffered from an influx of weapons smuggled in from the United States, and said the flow of drugs "is a problem of public health and consumption in your country's society."
Sheinbaum also criticized U.S. spending on weapons, saying the money should instead be spent regionally to address the problem of migration. "If a percentage of what the United States spends on war were dedicated to peace and development, that would address the underlying causes of migration," she said.
Sheinbaum's bristly response suggests that Trump faces a much different Mexican president than he did in his first term.
Back in late 2018, former President Andrés Manuel López Obrador was a charismatic, old-school politician who developed a chummy relationship with Trump. The two were eventually able to strike a bargain in which Mexico helped keep migrants away from the border — and received other countries' deported migrants — and Trump backed down on the threats.
But Sheinbaum, who took office Oct. 1, is a stern leftist ideologue trained in radical student protest movements, and appears less willing to pacify or mollify Trump.
"We negotiate as equals, there is no subordination here, because we are a great nation," Sheinbaum said, while adding, "I think we are going to reach an agreement."
But Gabriela Siller, director of economic analysis of the financial group Banco Base, fears the personality clash could escalate things into brinkmanship; Trump clearly hates to lose.
"Trump may have just tossed the threat out there, as he does," Siller said. "But Mexico's response, that we're going to respond to you with tariffs, that will make Trump really impose them."
It's not clear how serious Trump's threat is. The U.S.-Mexico-Canada free trade agreement forbids just imposing tariffs on other member countries. And it's not clear whether the economy could even tolerate sudden levies on imports: Auto plants on both sides of the border rely on each other for parts and components, and some production lines could screech to a halt.
"It is unacceptable and would cause inflation and job losses in Mexico and the United States," Sheinbaum said, while offering to talk about the issues. "If tariffs go up, who will it hurt? General Motors," she said.
"Dialogue is the best path to achieve understanding, peace and prosperity for our two countries," Sheinbaum said. "I hope our teams can meet soon."
Late Monday, Trump said he would impose a 25% tax on all products entering the country from Canada and Mexico, and an additional 10% tariff on goods from China, as one of his first executive orders.
The tariffs, if implemented, could dramatically raise prices for American consumers on everything from gas to automobiles to agricultural products. The U.S. is the largest importer of goods in the world, with Mexico, China and Canada its top three suppliers, according to the most recent U.S. Census data.
Trump made the threats Monday in a pair of posts on his Truth Social site in which he railed against an influx of illegal migrants, even though apprehensions at the southern border have been hovering near four-year lows.
"On January 20th, as one of my many first Executive Orders, I will sign all necessary documents to charge Mexico and Canada a 25% Tariff on ALL products coming into the United States, and its ridiculous Open Borders," he wrote.
He said the new tariffs would remain in place "until such time as Drugs, in particular Fentanyl, and all Illegal Aliens stop this Invasion of our Country!"
"Both Mexico and Canada have the absolute right and power to easily solve this long simmering problem. We hereby demand that they use this power," he went on, "and until such time that they do, it is time for them to pay a very big price!"