Adam Austen, a spokesman for Canadian Foreign Minister Chrystia Freeland, who is leading NAFTA trade talks for Canada, said the minister was in regular contact with her Mexican and USA counterparts.
"If we don't take advantage of this window of opportunity, it will close towards the end of the month, and the push would lose force and we'd need to look at another calendar" for getting a deal, Kalach said.
NAFTA talks are continuing in Washington this week between Mexico and the United States.
Trump, Lighthizer and Agriculture Secretary Sonny Perdue have publicly criticized Canada as uncooperative on USA proposals such as opening its dairy market to US exports.
Not a single US governor or senator has asked to pull their country out of NAFTA, Bachand said, which is Canada's true trump card in the negotiations, he added.
The nations are pushing for a deal by the end of this month in order to allow sufficient time for President Donald Trump and his Mexican counterpart, Enrique Pena Nieto, to sign the pact before President-elect Andres Manuel Lopez Obrador takes office December 1.
"If the US wanted a bilateral deal - and they don't, they've repeated often they want a trilateral deal - they don't have legal authority".
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The end of the tariff exclusions strained relationships with Canada, Mexico and the European Union, which responded with retaliatory tariffs on selected US goods.
Trump added that NAFTA has "been a disaster for our country".
It's all the more risky because of the short time frame in which Mexico and the US are looking to seal a trilateral agreement.
Quebec's premier said he had breakfast with the eastern premiers and New England governors and they "almost exclusively" talked about NAFTA.
U.S. -Canada negotiations will have to overcome the recent deterioration in bilateral relations following Trump's refusal to give Canada an exemption from steel and aluminum tariffs, and harsh criticisms directed at Canadian Prime Minister Justin Trudeau by Trump and his trade advisor, Peter Navarro.
United States officials have indicated that if the deal can be agreed by the end of August it would be possible to win congressional approval for the new NAFTA before Mexico's President-elect Andres Manuel Lopez Obrador takes office December 1.
Analysts who have been closely monitoring the talks say that USA and Mexican trade officials are working out details and that a deal still could unravel. The new rules also would include language aimed at having more cars and parts produced by workers who make wages well above the average low rates in Mexico.
Senator John Cornyn of Texas, the second-ranking Republican in the Senate, said he was more optimistic a deal on NAFTA would be reached after a recent phone conversation with Lighthizer.