Harrison also expressed hope the Liberals would abandon their stance that NAFTA had to be re-negotiated among all three of Canada, the us and Mexico and agree to participate fully in bi-lateral talks with the USA moving forward.
That means Canada could have as much as another 30 days to hammer out its part in the agreement, trade experts say.
Foreign Affairs Minister Chrystia Freeland, emerging Wednesday evening from her second meeting of the day with her US counterpart, said officials would be working late into the night - and possibly all night - on potential "landing zones" where both parties can agree.
The new trade deal between the USA and Mexico mostly makes revisions on auto, intellectual property and agriculture.
"We're hearing that there's a lot of progress being made and that it's possible that. we'll be able to see something sometime soon", Kevin Hassett, Chairman of the White House Council of Economics Advisers, told Fox Business Network on Wednesday.
Monday's announcement lifted equity markets in all three countries, with shares in automotive companies standing out on relief that the deal appeared to end the uncertainty that has dogged the sector for months. The offer, the report said, is part of an effort to save a dispute-settlement system within NAFTA, maintain safeguards for cultural industries and avert tougher pharmaceutical patent protections.
When a USA president intends to sign a trade deal with another country, he has to notify Congress in 90 days, and then Congress must approve it.
"I think with Canada, frankly, the easiest thing we can do is to tariff their cars coming in", Trump said. USA demands have ranged from ending those tariffs to scrapping a pricing system for milk ingredients that hurt US exports of milk proteins.
"We recognize that there is a possibility of getting there by Friday, but it is only a possibility, because it will hinge on whether there is ultimately a good deal for Canada", he said, speaking to reporters in Ontario.
The U.S. side favours a narrow timeframe for these latest trade talks, pushing for a deal by Friday.
Senior administration officials pointed to the deal as making both America and Mexico better off.
Will she be presiding over the death of the 24-year-old continental trade pact?
"Remember the visit from Prime Minister Trudeau to Washington, the message was, 'It's going to be very easy to solve the relationship with Canada.' The one that is complex and very hard is the relationship with Mexico", Guajardo said. -Canada issues, said it would be hard for Freeland to win concessions from Lighthizer on these issues.
Trudeau also said he would continue to defend supply management.
But Trump's trade representative, Robert Lighthizer, told reporters in Washington that the administration plans to push ahead with a U.S. -Mexico agreement, leaving Canada the option of joining in later. If after the review there is no consensus to renew, a review will be conducted every year until disagreements can be worked out and the parties agree to then renew for another 16 years.
The Trudeau government has repeatedly pledged to protect dairy farmers, but Canada has opened up limited access to its dairy market in previous trade talks, including its comprehensive pact with the European Union. "Mexico reserves the right to reform its energy laws, and it's laid down in writing that Mexico's oil and natural resources belong to the nation", he said.