Seattle’s mayor, Katie Wilson, gave a long, thoughtful response a few weeks ago when conversation at a Seattle University forum turned to the current economic climate and her support for higher taxes on wealthy residents and large businesses.

Then Ms. Wilson, a democratic socialist in her first year in office, went off the cuff: “I think the claims that millionaires are going to leave our state are super overblown,” she said. “And the ones that leave? Like, bye.”

Ms. Wilson’s comments generated applause and laughter in the room. But outside, the remarks drew a swift reaction and highlighted how political leaders and business executives are increasingly uneasy about Seattle’s changing relationship with the companies that helped transform the city into a global hub for entrepreneurial innovation. Her “like, bye,” and the wave she gave with it, also pulled Seattle into a broader debate in liberal cities about how to solve rising housing prices and economic disparity without driving away investment, employers and affluent residents.

In Seattle, the current debate centers on one company at the heart of its modern identity, Starbucks, which recently announced plans to create a 2,000-employee corporate hub in Nashville. Even before Ms. Wilson’s comments, anxiety was rising that the coffee giant — or at least more of its operations — could drift away from its hometown.

“I am gravely concerned,” said Rob Saka, a Seattle City Council member whose district includes West Seattle neighborhoods where many Starbucks executives live. “This is real.”

Ms. Wilson’s comments have drawn national attention to the worry among business leaders that Seattle doesn’t appreciate them, first from right-wing influencers, then mainstream outlets. Last week, Starbucks co-founder Howard Schultz singled out the mayor in a Wall Street Journal column accusing Ms. Wilson of “socialist rhetoric” that “vilifies employers, even while she continues to rely on them for revenue.”