In a telephone interview, Rubezhansky spoke of growing anger among Sochi residents. Discontent has spread countrywide as Sochi's budget has soared past $50 billion, an Olympic record and more than four times the original estimate.
Russian opposition leader Boris Nemtsov alleges that corruption among government and business leaders has accounted for $25 billion to $30 billion of that total. He calls the Sochi Games "the scam of the century beginning from the choice of venue and finishing with the crooked way it was implemented."
Nemtsov has also raised the specter of a terrorist attack.
In July, Chechen rebel leader Doku Umarov released a video encouraging Islamist militants in the northern Caucasus to target the Olympics. A suicide bus bombing in southern Russia last week heightened security concerns.
"I don't expect much from these Games but shame and humiliation," Nemtsov said.
People who follow the Olympic movement closely do not seem as alarmed by Sochi's struggles.
David Wallechinsky, who co-wrote "The Complete Book of the Winter Olympics," has chronicled decades of turmoil and controversy surrounding the world's grandest sporting event.
"There are always ups and downs beforehand," he said. "This is standard."
Preparations almost never go smoothly because the Olympics are massive, complex and enormously expensive. The winter version can be especially tricky for several reasons.
The events often require disparate sites: A cluster of mountain venues for skiing, snowboarding and sledding, plus a metropolitan complex of arenas for skating, hockey and curling. The vagaries of weather can further complicate matters.
As the late historian John Lucas once said, "Every single Winter Olympics has been fraught with problems."
In terms of weather, experts believe too little snow is preferable to too much.
At the 1998 Nagano Olympics, white-out conditions caused repeated delays in several marquee events. Conversely, when warm weather turned mountainsides into mush in Vancouver four years ago, organizers brought fresh snow from a colder locale.
Sochi has a similar plan, with hundreds of snow-making cannons and large reservoirs storing hundreds of thousands of cubic meters of snowfall from last winter.
"We have had enough time to learn the lessons of previous organizers," Chernyshenko said.
As for concerns about infrastructure and security, Wallechinsky sees political will working in Sochi's favor.
Russian President Vladimir Putin has made these Games a priority. Observers believe he will spend whatever is necessary to help Sochi succeed and keep it safe from terrorism.
"Of course there are some problems to be tackled," the president said in televised remarks from the city this week. "Some things need to be brought to conclusion, but there is confidence that everything will be done properly and in time."
It is doubtful Putin will want the anti-gay law to become an issue at his big show, despite the fact that at least one athlete is planning to wear a rainbow pin and others have vowed to speak out at news conferences.