KANSAS CITY, Mo.—The people of Kansas City thought they were getting a straight-shooter with financial smarts as their new mayor. What they got, critics say, is a henpecked husband who needs his wife to tell him what to do.

In an era when politicians get in trouble for infidelity, Mayor Mark Funkhouser finds himself under fire for his devotion to his wife, a sharp-elbowed New Yorker whose role as his closest adviser has locals wondering who’s really running this city of 450,000.

“I knew Mark for almost 18 years as auditor and didn’t even know he was married. It’s not like he needed his wife when he was auditor,” said City Councilman Ed Ford, a leading critic of Funkhouser and his wife, Gloria Squitiro. “I think we were all surprised that he felt she was so indispensable once he became mayor.”

Squitiro ran her husband’s campaign for mayor, and after he got elected last year, she took a desk near his office in City Hall.

That arrangement came to end soon after a former mayoral aide filed a lawsuit last summer in which she accused Squitiro of making lewd comments around the office and calling the aide, a black woman, “Mammy.”

The council responded with an anti-nepotism ordinance that bars Squitiro from volunteering in the mayor’s office. Funkhouser vetoed it, and the council overrode the veto. Funkhouser shot back by suing the city, saying the ordinance infringed on his authority.

He also began conducting a large share of city business from his home, stunning members of the council.

“I think government business should be done at City Hall and not out of the mayor’s home,” Ford said. “Part of it’s transparency. Part of it is ’Why is the mayor working out of his home?’ It’s obviously so Gloria can be by his side.”

The Kansas City Star, which backed his candidacy, retracted its endorsement last month. Funkhouser has also become a routine target of the paper’s editorial cartoons, including one this week that lampooned the power couple as “Nitro” and “Glycerin.”

In a letter to the editor this week, one reader said: “I didn’t see her name on the ballot. I don’t recall a two-for-one deal.” Another wrote recently: “He should be removed from office immediately so he can spend all of his time with his wife without his job getting in the way. Separation anxiety problem solved.”

Funkhouser said he and his wife are a political team. “The idea that I’m this infantile guy who’s tied to his wife’s apron strings and has to have her right there holding his hand—anybody who knows me knows that’s silly,” he said.

In an interview at the couple’s home on Thursday, Squitiro declared she has “never met a more manly man” than her husband, suggested her critics are annoyed by her brash personality, and said the couple’s team approach is her way of helping him succeed.

“I am working 70 hours a week for no monetary gain for myself to serve my husband because he has made promises to the people of this city that he’s going to keep come hell or high water,” she said. “And I’m here to serve him and make sure he keeps his promises.”