If the notification is not sent by May 17, U.S. House Speaker Paul Ryan has said that the Republican-controlled Congress likely would not have enough time to approve an update to the North American Free Trade Agreement before a newly elected Congress takes over in January.
Don't expect a NAFTA deal by this week's supposed target date.
Officials from Canada and Mexico were in D.C. last week working on the terms of a deal, but nothing was reached.
U.S. Representative Kevin Brady, the chairman of the tax and trade-focused House Ways and Means Committee, said there was probably little room to go past the Thursday deadline for a deal and still get a new NAFTA approved by year end.
Guajardo says the USA needs to show some flexibility on key NAFTA proposals, and he doesn't see it happening by Thursday.
United States House Speaker Paul Ryan set the cut-off date last Wednesday amid some optimism that Mexico, the USA and Canada could soon reach an agreement in principle as a result of meetings attended last week by the chief trade representatives in Washington.
"The possibility of having the entire negotiation done by Thursday isn't easy, we don't think it will happen by Thursday", Mexican Economy Minister Ildefonso Guajardo told the Televisa network, The Wall Street Journal reported.
A USTR spokeswoman, asked if the three ministers would meet again this week, said: "We have no announcements at this time".
Smith said the administration of President Enrique Pena Nieto had a responsibility to continue negotiating until Mexico's new president, who will be elected on July 1, takes office on December 1.
"We will keep negotiating, and in the moment that we have a good negotiation, we can close the deal and it will be notified, independent of which Congress [the current or new] that will vote on it", he said.
The current leading presidential candidate in Mexico, the progressive Andrés Manuel López Obrador, favors staying in NAFTA.
However, U.S. demands for a so-called sunset clause that would see NAFTA automatically expire if the agreement is not renegotiated every five years as well as the elimination of settlement panels for trade disputes remain sticking points.
"It could be before the Mexican election on July 1, it could be just after", he said.
He even revealed the details of a conversation on the subject between Prime Minister Justin Trudeau and President Donald Trump, who spoke by phone on Monday. Neither Canada nor Mexico wants that.
He also noted that negotiations may continue after the Mexican elections in July and a transition team would have to then be included in the talks.