Prime Minister Justin Trudeau, speaking at the Women in the World summit, was circumspect about the talks, saying only that he remains hopeful.
"I think we understand there are certain issues on which we will need to compromise", one of the sources said when asked about increased dairy access for the USA industry.
With the Mexico deal in hand, and Trudeau publicly indicating that Canada's red-line issues are Chapter-19 and cultural industries, the Americans have considerable leverage, he added.
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. She said she spoke with Lighthizer over the weekend and they agreed it would be useful for them to meet again face to face.
"We've taken those hits for team Canada, and we are determined that there be no further concessions on dairy", said David Wiens, vice president of the Dairy Farmers of Canada.
Last week, as the The Globe and Mail reported, Mr. Trump's trade chief, Robert Lighthizer, refused Ottawa's key demand, the preservation of the Chapter 19 dispute-resolution system, in order to extract maximum concessions from Canada on its protected dairy market and pharmaceutical patents.
No word yet on when she might return to Washington to continue NAFTA talks.
Wiens declined to say what action the organization would take if an updated NAFTA deal gave the USA a greater chunk of the Canadian market, but did not rule out campaigning against ratification of the agreement, or the Liberal government.
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.
After emerging from her meeting with Lighthizer on Friday, Freeland said the negotiations had entered a "very intense" phase, during which officials have been meeting "24-7".
Freeland is expected to answer questions from reporters later this afternoon. "But we don't negotiate differently because of pressure tactics like that".
As the two nations' chief negotiators prepared to resume their talks in Washington Tuesday, dairy producers suggest this deal is a line in the sand for them.
Freeland will spend Tuesday in the US capital before she heads to Saskatoon to attend Liberal caucus meetings that begin later in the day and run through Thursday.
US Ambassador to Canada Kelly Craft meanwhile delivered an address in Gander, Newfoundland, where dozens of in-bound flights were diverted in the immediate aftermath of the September 11, 2001 attacks.
Representatives from both sides have expressed their preference to keep a NAFTA deal intact.
What should Canada do at the NAFTA negotiating table?
Yet, he stressed that "if we sign the deal it'll be. for Canada and Canadians".