“Masseuse,” Offerman suggested from behind the wheel.

With a set list incorporating P.M. Dawn’s funky “Shake,” Ruth Brown’s bawdy “If I Can’t Sell It, I’ll Keep Sittin’ on It” and the classic George Jones weepie “He Stopped Loving Her Today,” Nancy and Beth’s poker-faced, very funny vaudeville — the act is choreographed, too — bridges the plush cabarets of the traditional American Songbook and a downtown scene where recontextualized interpretations of hits old and new flourish. Reflecting that range, the band has played the Newport Folk Festival, the Grand Ole Opry, “dives that didn’t have a bathroom,” per Mullally, and the posh New York City boîte Café Carlyle, where Nancy and Beth return for a two-week stint starting Tuesday.

Hunt and Mullally met in 2012 on the set of the indie film “Somebody Up There Likes Me,” in Hunt’s hometown Austin, Tex., and quickly discovered they shared an interest in music. In addition to being a show-tune pro whose Broadway credits include “Young Frankenstein,” Mullally headed the combo Supreme Music Program, which released three albums between 1999 and 2007. Hunt’s bass playing helped her get cast in the “Friday Night Lights” series as Devin Boland, a member of the high school metal act Crucifictorious.

As Mullally was about to leave Austin to visit her mother in Oklahoma City, the two women realized one more thing. “Stephanie had brought her ukulele and she told me she wrote songs,” Mullally recalled. “I said, ‘Let’s get in my air-conditioned rental car and I want to hear some of your songs.’ She said there was this one part I had to sing with her. She taught me the part and the minute we heard our voices together …”

The next thing they knew, they were in a band (which includes neither a Nancy nor a Beth). They released a self-titled album two years ago, and have crisscrossed the country, usually backed by a quintet of ace musicians from Los Angeles, Austin and New York that includes the violinist and singer Petra Haden, formerly of the indie rock band That Dog.