That deadline was put in place by House Speaker Paul Ryan in hopes the GOP-led Congress will vote on a renegotiated deal before the midterms.
"We don't think it will happen by Thursday".
The latest survey comes as U.S., Mexican and Canadian negotiators expressed increasing pessimism that they can come up with a re-write of the 1994 NAFTA accord demanded by President Trump in the coming days.
Trade negotiators for the United States, Canada and Mexico are running out of time to complete an overhaul of the North American Free Trade Agreement, making it likely the effort won't be completed this year.
Chief Mexican NAFTA negotiator Kenneth Smith said that the administration of President Enrique Pena Nieto had a responsibility to keep 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. independent of which Congress [the current or new one] that will vote on it", he said.
Mexico's peso sank to its weakest level in over a year on Tuesday, and the country's benchmark stock index fell about 1 percent to its lowest since early April.
Guajardo said it was not yet clear when the ministers from Mexico, Canada and the United States responsible for negotiating NAFTA would meet again.
Audio clip spurs social media debate over Yanny or Laurel
Why would people hear two totally different words? Experts say the fierce debate all has to do with sound frequency. Older individuals tend to not have as great of a high frequency range, so they may be more likely to hear "Laurel".
Mexico's economy minister Ildefonso Guajardo reiterated that Thursday was not a feasible deadline.
Guajardo said that negotiators were close to reaching agreement on rules of origin for the auto sector.
Among the issues the three sides have yet to agree on is a US proposal to include a so-called sunset clause that would allow the deal to automatically expire every five years, pending renewal.
"The ball is in their court", one Mexican government official said of the Americans when asked about next steps for the NAFTA talks.
More flexibility was needed for a deal, Guajardo said.
Democratic Rep. Rosa DeLauro of CT on Wednesday urged negotiators to continue their talks, saying Ryan's deadline is arbitrary.
Hanging over the talks is Trump's threat to impose steel and aluminum tariffs on its trade partners.
"Mexico's position since the start of the negotiation has been that we're not going to sacrifice the quality of the deal to conclude quickly", he said, although he added that there is still time to reach a conclusion before the end of the year.