Lighthizer spent Monday in Brussels for trade discussions with the European Union - preliminary talks that are scheduled to resume later this fall.
"For this government to go out and be seen as giving too much to the American side on agriculture, and dairy in particular, would be ... nearly suicidal politically", Charest said.
After her stop in Washington, Freeland is due to attend this week's meetings of the governing Liberal Party of Canada in Saskatoon, Saskatchewan.
"We agreed that it would be useful to continue talking today, so we're back for more negotiations", Freeland told reporters as she entered the USTR offices in Washington.
The current NAFTA's dispute resolution mechanism, known as Chapter 19, allows companies that feel their products have been impacted by anti-dumping or countervailing duties to request arbitration.
David Wiens, vice president of the Dairy Farmers of Canada lobby group, said Canadian farmers have already given up around 5 percent of a domestic market worth around C$21 billion ($17 billion).
Solemn cross-border remembrances slammed headlong into the present-day fight over free trade Tuesday as Canada and the US resumed their protracted effort to rescue NAFTA on the 17th anniversary of the September 11 terrorist attacks in Washington and New York City.
The uncertainty over the fate of NAFTA, in light of a tentative U.S. -Mexico trade deal, has not gone away even as trade experts note that members of Congress, concerned about the trade ties between the two countries, may help ensure that a final deal includes Canada.
"Our baseline is that Canada will join the U.S. -Mexico agreement, making concessions on dairy, but that it likely will have to make some concession on dispute resolution as well".
Data released on Wednesday showed the USA trade deficit hit a five-month high of $50 billion. "It appears as if there is not a whole lot of momentum right now".
The two sides have so far been unable to resolve key differences over USA access to the Canadian dairy market, a cultural exemption for Canada and the Chapter 19 dispute resolution mechanism. "There is progress made".
Uncertainly over the future of NAFTA, which underpins $1.2 trillion in trade, is weighing on markets as well as the Canadian and Mexican currencies.
Still, "with a bit of flexibility, things could move quickly", the source added.
Mr. Ujczo said he doesn't believe Mr. Trump feels strongly about Chapter 19. "But right now the USA position is to squeeze every last drop in concessions".
In Michigan, 259,000 jobs depend on trade and investment with Canada, the study said. "Canada wants to make a deal".
Canadian Prime Minister Justin Trudeau, from US President Donald Trump, has unanimous domestic support for now but to keep a firm hold on power must wring concessions from an unwilling powerful dairy lobby in order to mollify Washington.
"There's an opportunity to update NAFTA and we're happy to do it, but as I've said it has to be the right deal, it has to be a good deal", he said.
"We're just going to stay working constructively to get to that win, win, win that we know is there".