Lighthizer said that there "is still a fair amount of distance between" the USA and Canada.
Freeland's spokesman, Adam Austen, said Canada would only sign a good deal.
The U.S. and Canada are at odds over anti-dumping dispute panels contained under Chapter 19 of the current deal, which the U.S. wants to remove and Canada wants to keep.
U.S. and Canadian negotiators have spent more than a month trying to resolve remaining differences after Washington sealed a tentative deal with Mexico City which they intend to sign by December 1, when a new Mexican government takes office. Trudeau spokeswoman Chantal Gagnon said: "No meeting was requested".
The U.S. has been holding negotiations with Canada after reaching a trade agreement with Mexico in August.
The US and Canada are basically out of time to iron out their differences in a trade agreement before the Sept 30 deadline to have a completed full text. "And frankly we're thinking about just taxing cars coming in from Canada", he said.
The US administration has recently turned up the heat on Canada, trying to push for a concluded deal by this Sunday or else Canada risks being left out of a revised NAFTA agreement.
"I think everybody knows what each other's position is on all of the major issues and I think it's really a question of whether or not the US wants to have a deal".
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Trudeau also said the tariffs that Trump imposed on Canadian steel and aluminum in late May would have to be scrapped before Canada felt comfortable signing a new NAFTA.
But he said: "I believe this US-China discussion will go on for a while".
Whether Congress will pass a deal that doesn't include Canada remains unclear.
"I'm anxious a little bit that time will catch up with us", he said at a luncheon, noting that he had spent more time in Washington DC working on trade issues than ever before.
Flavio Volpe, the head of Canada's auto-parts industry lobby, said Mr. Lighthizer was moving the goalposts and that Canada should hold the United States to its original promise that a NAFTA deal would mean no tariffs. "I think there's a possibility there to build on what they agreed".
Trudeau said the deal between the USA and Mexico raises the "possibility" of Canada signing on, but that he's standing up for Canadian interests in negotiations. "It was an interaction like so many are (at the) United Nations - quick but cordial. We don't like their representative very much", Trump added.
"I'm anxious a little bit that time will catch up with us", he said, noting that he had spent more time in Washington working on trade issues than ever before.
