Talks between the city and the union representing its outside workers extended well past the scheduled 12:01 a.m. deadline Sunday, offering some hope that the two sides might be close to a deal.

A CUPE spokesperson announced that the deadline would be extended to 2 a.m. Sunday, which came and went with both sides remaining behind closed doors at a downtown hotel.

The turn of events followed word late Saturday that Deputy Mayor Doug Holyday would not agree to meet with CUPE's national president.

CUPE president Paul Moist, whose local union 416 represents Toronto's outside workers, called for a meeting with Holyday in a bid to tone down the rhetoric of the labour talks.

However, Holyday told CP24 that he had no intention of meeting with Moist.

"I will not be meeting with the CUPE president," Holyday said in a telephone interview with CP24 early Saturday evening. "This is just another distraction. They keep calling these press conferences, but what they really need to do is to sit down at the table and get down to the brass tacks and negotiate a contract. You can't keep putting these distractions in the way and then hope to have success."

The call to meet with Holyday came as the war of words between the groups heated up over the past few days. The city is in a legal position to lock out the workers, who in turn have the right to walk off the job, on Sunday morning if an agreement is not reached.

"In requesting to sit down with Deputy Mayor Holyday, the entire purpose of that is to refocus the efforts of everybody concerned at this juncture to come up with a collective agreement and maybe tone down some of the words being used," Moist said during a press conference at a downtown hotel Saturday.

"We would move discussions between the city and CUPE at a senior level away from op-eds, away from media releases and it might bring down the tone of the discussions to one of problem solving."

Earlier in the day, Holyday published an opinion piece in some newspapers that said the current round of negotiations was the city's "crucible" and is shaping up to be "the defining experience" in Toronto's recent history. He also said that the results of the contract talks will have "ripple effects throughout Canada."

"I think the kind of tone in the community here in Toronto has been quite loud and in my view not helpful. But it is what it is and that is why we are reaching out here today," Moist said.

"I'm not sure that there is a ripple effect throughout Canada by what is going on in Toronto right now."

CUPE 416 president Mark Ferguson accused the city on Friday of attempting to bully the union and its 6,000 workers with a last chance proposal and said the city has no interest in working out a collective bargaining agreement.

"Simply put the city has decided it is better to be a bully than a problem solver," Ferguson said Friday.

The city countered by releasing on Friday a detailed list of what it has put on the table to the union in an attempt to show the public what is at stake.

This included a 1.25 per cent lump sum wage payment in 2012, a 1.5 per cent lump sum payment in 2013, a 1.75 per cent lump sum payment in 2014, and a 1.75 per cent base wage increase in 2015.

It also would also remove an agreement regarding the so-called "work-for-life" guarantee.

The union had offered to take a three-year wage freeze.