Voters in the Swiss canton of Graubuenden, where both towns are located, will decide in a referendum on Sunday whether or not to support the bid.
It would be a first for Davos while St Moritz, home of the Cresta run and the annual polo World Cup on snow, would be hosting the games for the third time after 1928 and 1948.
Organisers want to bring the winter Olympics "back to the mountains" after the city-based Games in Turin, Vancouver and upcoming Sochi but are having a hard time convincing the local population.
"We want to bring the winter Olympics back to the snow, it would be great if you could sit in the hotel and watch it snowing outside," Joerg Schild, president of the Swiss Olympic Committee, said.
"Turin is a beautiful city, but it took two hours by car to get to the Alpine sports venues. Vancouver was a fantastic games but it was 1-3/4 hours to the mountains."
Graubuenden 2022 organising committee member Gian Gilli added: "I was in Sochi recently and it was 18 Celsius in winter."
But even the organisers admitted that the referendum, the first hurdle the bid must pass on its way to the International Olympic Committee, was on a knife-edge. "It will be very close," said Schild.
The bid organisers argue that the estimated investments of 4.3 billion Swiss francs (£3bn) will be repaid by the boost in tourism which will result from staging of the event.
Of this, 1.5 billion (£1.1bn) would be on transport on sporting infrastructure and 2.46 billion (£1.74bn) would be on running the game.
They say that the bid is sustainable and environmentally friendly and that much of the necessary infrastructure already exists.
Opponents fear the environmental impact of new buildings, ski lifts and other infrastructure on the Alpine environment. They are also are concerned that the initial budget will spiral out of control, as invariably happens with major sporting events.
"This is an enormous chance to give tourism a big boost in the region," Sigi Asprion, head of the St Moritz town council, said.
"If we can we show ourselves as a place for winter holidays, the whole of Switzerland will benefit."
Tarzisius Caviezel, the head of the bid, rejected any suggestion it would be environmentally destructive.
"This is an unfounded criticism because, from the start, we have given great importance to this ecological aspect and we have ensured that not one piece of wood will have to be pulled up," he told Reuters.
"The construction of temporary structures in the village area will be done with great care, so no environmental damage will be caused."
But the locals are still worried.
"Pressure to say yes to this has been enormous, including from public officials, but I think that pressure in recent days has shifted to the bid committee," Juerg Grassl, an architect who lives in Davos and works in Chur, told Reuters.
He said that promises such as federal subsidies for the single-track, narrow gauge Rhaetian railway which serves the reason have not panned out.
"It doesn't make sense financially, it's much too large an event, and it would burden the region with about 175,000 additional guests daily, about 10 times what we get on a booming day," he said.
Karin Bravo, a 41-year-old opticians' receptionist from Davos, said the region was too small for such a big event.
"I find it too risky. It's much too large an event for Davos and St. Moritz alone, but would be all right if it was carried out in all of Switzerland," she said.
"I was almost swayed by the good concept the bid committee put together, but the costs are opaque and it will incur a lot of debt."
She said another problem was affordable housing in Davos, already suffering from event fatigue from its annual hosting of the annual World Economic Forum.
"If the bid is accepted, it will mean a lot of construction, which would jeopardize our summer tourism season. The Olympics won't make up for that shortfall."
The vote will be held on the same day as the so-called "Fat Cat" nationwide referendum on executive wages where voters will be asked whether shareholders should have a binding say on pay and ban "golden handshakes" for new arrivals and "golden parachutes" for departing managers.
Caviezel said he welcomed the debate as an example of Swiss grass-roots democracy.
"It shows we really live in a democracy where everyone can voice their opinion," he said.
- Sports & Recreation