Central considerations are the ability of the host committee to raise money to pay for the event, the number of hotel rooms and the calendar. Republicans want to avoid the mistake of 2012 when they waited until August, depriving Mr. Romney of general-election funds to counter a summer of Democratic attacks. Cleveland promises it could hold a convention in June, and Dallas in July. “Either date would be a step in the right direction,” Mr. Mahoney said.

The Republicans promise a final decision next month. If they select Cleveland, the Democrats, who are not planning to choose until later, will strike the city off their list.

Jim Swift, a native of Shaker Heights, a Cleveland suburb, who worked on logistics at previous conventions, threw cold water on boosters’ hopes in a column in The Plain Dealer. He warned of snarled traffic, violent protests and the unlikelihood of a “media narrative” about a Cleveland comeback. “The media love to complain, and complain they will,” he wrote.

Talk of a Cleveland revival has been fanned before. It came two decades ago with the opening of the Rock and Roll Hall of Fame and downtown renewal that included the 20,500-seat arena where the Cleveland Cavaliers play, which would be home to the party hats and balloons of a nominating convention.

But that optimism was flattened by other headlines about the city: the loss of 17 percent of its population registered in the 2010 census, a cascade of foreclosed homes in poor neighborhoods during the financial crisis, and sensational crimes like the imprisonment of three women for a decade by a man whose neighbors never noticed.

“The phrase that’s used here more than anything else when talking about how Cleveland’s doing is, ‘At least we’re not Detroit,’ ” said Daniel McGraw, a city native who writes for Belt Magazine, an online publication that finds glamour in the city’s grit.