Prime Minister Justin Trudeau, speaking at the Women in the World summit, was circumspect about the talks, saying only that he remains hopeful.
He and other American politicians have long demanded Canada's system of domestic dairy protections either be abolished or heavily modified to give USA exports a bigger share.
U.S. President Donald Trump said at the White House that trade talks with Canada were going well and that Ottawa wants to make a deal.
"I spoke with Ambassador Lighthizer over the weekend", Freeland said.
"Even if we gave him everything he wanted - and there is no way we would ever do that - who can say whether he'd be satisfied?" said one source, who declined to be identified given the extreme sensitivity of the situation.
In return for concessions on dairy, Canada could request USA concessions on the so-called Chapter 19 dispute resolution mechanism that allows Canada to combat US anti-dumping duties that Ottawa regards as unjustified.
The in-person, high-level negotiations got back underway as events marking the 17th anniversary of the 2001 attacks took place around the USA, including at the Pentagon with Vice President Mike Pence, not far from where the trade meetings are taking place.
"There's a range of things we've been firm on and will continue to be firm on, but there's also things we're looking to be flexible on because it's time to update this deal after 25 years", he said in an interview with Winnipeg radio station CJOB. "But we don't negotiate differently because of pressure tactics like that".
Heavy rain expected for Toronto starting Sunday night
Rain moving in will become heavy at times Saturday night over western areas, and become heavier over eastern areas on Sunday. We have avoided significant rainfall for most of the area so far this month but that changes quickly starting this evening.
Talks were expected to resume this week between the two.
After her stop in Washington, Freeland is due to attend this week's meetings of the governing Liberal Party of Canada in Saskatoon, Saskatchewan. "I think everybody is working towards a deal", said Flavio Volpe, president of Canada's Automotive Parts Manufacturers Association. "You can't fix NAFTA without fixing issues with Canada", said Senator Ron Wyden, the top Democrat on the Senate Finance Committee, which oversees trade.
What should Canada do at the NAFTA negotiating table?
"Having said all of that, nothing is done until everything is done" - and that says it all really, but US officials have said time is running out to agree on a text that can be signed by American, Canadian and Mexican leaders by November 30, before the current Mexican government leaves office.
Daniel Ujczo, a USA trade lawyer who has worked for both the Canadian and the US governments, rejects the notion that Canada and the United States are at a stalemate.
"If (Trump) goes to Congress with a bilateral arrangement with Mexico, he's got problems - real problems", Mulroney said.