Yet others believe that Mr. Ganim, 58, will do well at the party’s nominating convention this spring. They cite the breadth of his delegate support in Bridgeport, a gritty coastal city of 150,000 where he has earned praise for attracting development, stabilizing finances and bolstering the police.

Even if Mr. Ganim does not win the party’s nomination, which requires more than 50 percent of the delegate vote, he could garner the 15 percent needed for a spot on the primary ballot. Failing that, he would have to obtain thousands of petition signatures, something he pledges to do.

“Democrats are saying, ‘Holy cow, this can’t happen,’ ” said Peter Spain, a Democratic member of Bridgeport’s City Council and a longtime critic of Mr. Ganim. “It’s wrong for someone who totally betrayed the public trust to come back and shrug it off and act like the people of Bridgeport forgave him.”

Many in Bridgeport did forgive him, however. In 2015, Mr. Ganim managed to defeat the incumbent mayor, Bill Finch, in the Democratic primary and went on to beat his closest opponent in the general election by two-to-one.

That same year, Bridgeport conducted a citywide tax reassessment that revealed a sobering trend. The value of Bridgeport’s taxable property had fallen by a staggering $1 billion, to $6 billion. That — coupled with a $20 million budget deficit left by the previous administration — prompted the city to raise the effective tax rate on properties by nearly 29 percent.

As he has traveled the state in recent months, Mr. Ganim said he found that residents do not necessarily share his critics’ view that his message only plays in the state’s urban centers. “They have a viewpoint that my candidacy may sell in Bridgeport, but it won’t in Mayberry,” he said, referring to the 1960s sitcom “The Andy Griffith Show.”