WASHINGTON – The chairman of a key congressional committee warned Thursday that he would take steps to block new tariffs against Mexico if President Donald Trump follows through on his plans to impose the duties early next week.

“The president’s proposed tariffs would hurt American workers, businesses and consumers,” said Rep. Richard Neal, a Massachusetts Democrat who chairs the House Ways and Means Committee. “If the president does declare a national emergency and attempt to put these tariffs into place, I will introduce a resolution of disapproval to stop his overreach.”

Neal’s warning was the latest sign of the domestic backlash Trump is facing over his tariff threat and comes as the U.S. and Mexico are involved in a second day of high-stakes discussions in hopes of reaching a deal to avoid the duties.

Trump has threatened to slap 5% tariffs on all Mexican imports, starting Monday, unless the Mexican government stops the flow of Central American migrants coming to the U.S. southern border. He has vowed to increase the tariffs 5 percentage points a month, until they reach 25%.

Vice President Mike Pence and Mexico's Foreign Affairs Secretary Marcelo Ebrard led an initial round of negotiations on Wednesday, but those failed to produce a breakthrough. The talks resumed Thursday morning at the State Department, where Ebrard spent nearly three hours behind closed doors with Trump administration officials.

“I think we are making advances,” the foreign minister told reporters as he left the building.

Although Trump said he would impose the tariffs on June 10, that may be a soft deadline. Trump has delayed similar threatened actions before, such as tariffs of China, citing ongoing negotiations as a justification.

White House spokeswoman Sarah Sanders downplayed the possibility of a delay.

"We are still moving forward with tariffs at this time," she said Thursday afternoon.

Pence expressed optimism about a possible deal, but stressed that the Mexicans need to do more.

“As President Trump has made clear, we have a crisis on our southern border,” Pence said. “…The president has taken a strong stand. We’ll continue to take that strong stand until Mexico takes such action as is necessary to address this crisis and bring this crisis of illegal immigration at our border to an end.”

The U.S. Border Patrol announced on Wednesday that authorities had apprehended 84,542 members of family units crossing the southwest border with Mexico, the fourth straight month the agency has broken its record for family arrests.

That represents a 44% increase from April’s total of 58,724 family members caught crossing the border, a clear indication that Trump's efforts to stop the flow of migrants across the southern border are not working and that Central American families are continuing their march north.

Ebrard and other Mexican officials note that Mexico has already enacted strong measures to curb migration, by cracking down on human smuggling and returning more than 80,000 migrants crossing through Mexico to their home countries.

"Without Mexico’s efforts, an additional quarter-million migrants could arrive at the U.S. border in 2019," Martha Barcena, Mexico's ambassador to the U.S., told reporters at a news conference earlier this week. Slapping tariffs on Mexico, along with the Trump administration's decision to halt aid to Central American countries, is "counterproductive," she said, and will not reduce migration flows.

Top Republicans in Congress have warned the Trump administration against imposing the new tariffs, saying the president risks an embarrassing congressional reversal if he goes through with the plan.

Contributing: David Jackson and Alan Gomez

More:'A giant game of chicken': GOP lawmakers warn against Trump's threatened tariffs on Mexico