In a meeting with Democratic lawmakers on May 16, U.S. Trade Representative Robert Lighthizer downplayed the possibility of a pared-down or "skinny" NAFTA agreement while acknowledging some "backsliding" in the talks with Canada and Mexico.
Mexico's economy minister Ildefonso Guajardo reiterated that Thursday was not a feasible deadline.
He has not met with his NAFTA counterparts since last week.
U.S. House Speaker Paul Ryan had said that the Republican-controlled Congress would need to be notified of a new deal by Thursday to give lawmakers a chance to approve it before a newly elected Congress takes over in January.
Sarah Huckabee Sanders, the White House press secretary, declined on Thursday to comment on continuing negotiations but said that, on immigration, "the president does want to see Mexico step up and do more".
Representative Gerald Connolly, a Virginia Democrat, also said that Lighthizer "indicated it is unlikely that an agreement would be reached by tomorrow".
"An very bad lot of things would have to go right in order for this to be voted on in this Congress", said Eric Miller, a Washington-based trade adviser and Woodrow Wilson Center fellow.
If no deal has been agreed upon before December when he will potentially take office if he wins the election, he is likely to replace the entire Mexican negotiating panel - and sending the entire process into reverse - the pact that has governed cross-border trade since 1994 will be way back up in the air once again and that is bearish for both the Loonie and the Mexican peso.
"The point is, we can't work a bill unless we have an agreement that's in writing that we can work on, and that hasn't occurred yet", Ryan said. Canadian Foreign Affairs Minister Chrystia Freeland's spokesman called the deadline a USA issue.
Trump could decide to leave NAFTA entirely. She told reporters Wednesday that May 17 was an "arbitrary" date and that the real deadline for a 2018 vote was "probably around mid-June".
But negotiators remain far apart on several key issues, involving domestic auto content, dispute resolution and whether to impose a "sunset clause" requiring periodic renewal of the treaty.
But here is the thing - While nations such as Canada and the U.S, might be feeling positive about NAFTA, Mexico is a different bag of "frijoles" altogether.