The Canadian city was one of seven bids for the Games confirmed by the International Olympic Committee (IOC) yesterday.

A Council vote over whether to press ahead towards pursuing a bid last month had passed by eight votes to six, meaning that a switch from one member would erase any majority.

Diane Colley-Urquhart, one of those previously in support, has now said that there are "a lot more risks today than there were two weeks ago".

"I'm getting more concerned as this thing moves forward, with the strings attached to the money and imposing on the municipality," she told reporters.

"I'm open to a reconsideration motion [of her support] given the untenable situation we've been put in."

Calgary Mayor Naheed Nenshi has estimated that it would take at least four to six months to set up a potential referendum on whether to press ahead.

This gives little wriggle-room given the IOC Session is due to vote on which bids to take forward to the candidate stage in Buenos Aires in October.

Provincial and Federal Governments confirmed last week that they would financially pledge a combined CAD$10.5 million (£5.8 million/$8.1 million/€6.6 million) to support the formation of a Bid Corporation.

This does not mean they will necessarily end-up supporting the bid, however, only that they are open to further assessment.

Colley-Urquhart also questioned the logistics of holding a referendum and the decision to announce the Government support shortly before a holiday weekend.

"If we proceed to take this money, to explore this notion, do we actually have enough time to get the information out to Calgarians to make an informed decision on this," she added.

"It's almost untenable. 

"It's almost as if we're being backed into a corner with our own money."

An Ipsos poll published by Global News this week claimed that 92 per cent of local citizens would back a privately funded bid and found that 56 per cent believe there are more benefits than risks to hosting the 2026 Olympics.

Sixty-six per cent of those surveyed in a poll of 1,303 Canadians last month, however, reportedly believe the city would risk going into "serious debt" if it hosted the 2026 Games and only 49 per cent would be happy for taxpayers' funds to be used.

IOC executive director for the Olympic Games, Christophe Dubi, insisted they would have no problem with a referendum in Calgary or any other city.

"We don't see a problem with this, on the contrary," Dubi said.

"If there is a public consultation, it has to welcomed. 

"A project of this nature has an impact, hopefully a positive impact, on the lives of the citizen for a long term duration."

A Committee is now due to decide whether to pledge another CAD$2.5 million (£1.4 million/$2 million/€1.6 million) of funding to Calgary on Tuesday (April 10).

Graz in Austria, Sapporo in Japan and Stockholm in Sweden are among the other contenders.

They are joined by Sion in Switzerland, Erzurum in Turkey and a joint Italian bid from Milan, Turin and Cortina d'Ampezzo.

A host is due to be chosen in 2019.