Sources close to the talks have told CBC News that Canada views the proposal as a "non-starter".
Although sources briefed on the talks describe the mood as sour, Mexican and Canadian politicians say there is no question of leaving the table for now.
Among those he met Thursday were groups active in advancing reproductive choice for Mexican women - in January, U.S. President Donald Trump reinstated and expanded the controversial "Mexico City Policy" that bans using foreign aid for abortion-related activities.
Trump has made no secret that he prefers bilateral trade deals, and skeptics wonder whether the USA demands are part of an "America First" strategy created to ensure the current talks fail. With that in mind, he said he's warned US trade representative Robert Lighthizer to tread carefully around the sector.
He explained that Mexico is already preparing a back-up plan if NAFTA "goes sideways".
Business leaders from all three countries have said the USA proposals could derail the talks.
His comments came after Canada's producers lowered their prices for dairy ingredients to make them more competitive against cheaper American imports.More news: What Argentina need to do for 2018 FIFA World Cup qualification
The United States also wants to boost how much North American content autos must contain to qualify for tax-free status and modify dispute settlement mechanisms.
"NAFTA is not going anywhere".
Canada and Mexico want their companies to be able to bid on more US federal and state government contracts, but this is at odds with Trump's "Buy American" agenda.
Despite clear signs of impatience from Canada in particular, USA negotiators have yet to submit their proposal on rules of origin for the auto sector.
Trump on Wednesday repeated his warnings that he might terminate the pact and said he was open to doing a bilateral deal with either Canada or Mexico.
Ahead of the fourth round of talks, U.S. Agriculture Secretary Sonny Perdue hinted the U.S. would be looking for increased access to Canada's dairy.
But the Americans also want a country-specific change that would increase USA content requirements to 50 per cent in the first year of the new deal.