LAS VEGAS — From her glass office at the top of City Hall, Mayor Carolyn G. Goodman looked down at the transformation of this city’s once-crumbling downtown, nodding toward new attractions — the eye-catching brain research center, the Mob Museum, the sprawling performing arts complex — as evidence that Sin City is no longer just about booze and blackjack.

But Las Vegas is missing one essential ingredient, she said: major league professional sports.

With about two million people, the Las Vegas Valley is one of the last major metropolitan areas without a team of its own, in part because big-league sports teams shy from tying themselves to a gambling town. Now, Las Vegas could be poised to land one: a Major League Soccer franchise, which would play in a new downtown stadium.

But the public has not yet embraced this vision of Las Vegas. Instead, residents have revolted against the prospect of paying for the stadium with tax dollars. Without millions in public money, it is unlikely that shovels will hit the dry ground on the $200 million project.

The stadium’s future now depends on a final City Council vote in December. Ms. Goodman has pleaded with residents to “believe in Las Vegas,” arguing that the vote is about the kind of city that Las Vegans want to have.