(CNN) American importers are warning the White House and members of Congress that a logistical nightmare could unfold if President Donald Trump follows through on his threat to impose tariffs on all Mexican imports starting Monday.

"The simple plumbing of trade is not something that some of these companies are familiar with or that they're set up to immediately start using," John Murphy , senior vice president for international policy at the US Chamber of Commerce, told CNN. "The writing's on the wall already that many simply will not be ready to pay duties beginning on Monday."

"We are still moving forward with tariffs at this time," White House press secretary Sarah Sanders said late Thursday, after two days of talks produced no immediate results.

Officials said the final decision rests with Trump, who is scheduled to return on Friday from his European trip to commemorate D-Day and has been regularly briefed on negotiations while overseas. He pledged a week ago to ratchet up tariffs, starting with a 5% levy June 10 and topping out at 25% by October.

As of Thursday, US Customs and Border Protection had still not received guidance necessary to implement the tariffs, including details like software changes for automated systems that process the customs entries, according to trade and customs attorney Lenny Feldman, who is on CBP's commercial customs operations advisory committee.

He said there are also lingering questions for customs officials about which goods will be impacted by the new tariffs.

"What about US content in returning Mexican goods?" he asked, referring to goods manufactured in Mexico with US components.

Typically, the White House would allow time for agencies and importers to sort out the changes, but with the tariffs not yet finalized, businesses will have only the weekend to work out any changes.

The sudden threat has sent American importers scrambling to prepare. Mexico is one of the top US trading partners, with nearly $1 billion in goods crossing from Mexico into the United States per day in 2018. That includes cars and machinery as well as agricultural products.

The 25-year-old North American Free Trade Agreement gradually eliminated the vast majority of tariffs between the US and Mexico, leaving many importers unprepared to pay the new duties if they go into effect.

In a letter Wednesday to US Trade Representative Robert Lighthizer and the Department of Homeland Security, the Nogales US Customs Brokers Association warned that "it will be impossible" for companies to comply with the coming tariffs because "the mechanisms for compliance are not available between now and June 10."

"Without commenting on the policies of the Administration, we ask USTR, DHS, and CBP, and of course the President, to postpone any new import duties on product from Mexico, until CBP can develop the procedures by which importers and brokers can reasonably pay them," Nogales US Customs Brokers Association President Fernando Sandoval wrote in the memo.

One issue is that many importers don't have accounts to pay tariffs. CBP has warned of growing backlogs of up to three weeks for new applicants, according to the association's letter.

"CBP is working through details, including the technical aspects, to implement tariffs when directed," a CBP spokesperson told CNN on Thursday.

Republican senators have expressed frustration with the administration's lack of clarity on the plan.

On Tuesday, officials from the White House counsel's office and the Justice Department met with members during the GOP Senate lunch to discuss the legal reasoning behind Trump's use of national emergency powers to wield the tariffs. Senators came away from the lunch unsatisfied.

Senators have urged Trump to delay the tariffs until he has returned from Europe and can brief them directly about the strategy -- including how the tariffs will impact negotiations over the President's replacement for NAFTA, the United States-Mexico-Canada Agreement.

"We need to sit down with the President and talk about the way forward, because I think this has a number of challenges, not the least of which is the USMCA," Republican Sen. John Cornyn of Texas told CNN on Tuesday night.

Republicans were still holding out hope that the tariffs -- and a potential showdown between Congress and the White House -- could be averted, as talks continued late Thursday.

"Let me just say there is a lack of enthusiasm among Senate Republicans for what would amount to a tax increase, frankly, on working class people," Senate Majority Leader Mitch McConnell said in a radio interview with Fox News' Guy Benson on Wednesday afternoon. "I'm hoping this can be avoided."