In 1991, Higgins was featured in Broadway's La Bête and, in 2000, he was seen Off-Broadway at Second Stage Theatre in a production of Edward Albee's Tiny Alice. He also originated the title role in Paul Rudnick's Jeffrey Off-Broadway in 1994.
Higgins' numerous television credits include recurring characters on Ally McBeal, Brother's Keeper, Boston Legal and Honey, I Shrunk the Kids: The TV Show. In Season 8 of Seinfeld, he portrayed Elaine's boyfriend Kurt. He also played attorney Wayne Jarvis in five episodes of Arrested Development. Higgins arranged the dense vocal harmonies sung by the nine-part ("neuftet") New Main Street Singers in 2003's A Mighty Wind, a change from the writers' original concept to have the group sing in unison, leveraged by Higgins' musical talent.
Recently, Higgins has gained more recognition by being featured in the films Fun with Dick and Jane and The Break-Up, for which he also wrote vocal arrangements. His work as a voice actor includes the role of Judge Mentok in Harvey Birdman, Attorney at Law and 2401 Penitent Tangent in Halo 2 and Riddler in Batman: The Brave and the Bold. Higgins is also remembered for portraying David Letterman in the HBO TV film The Late Shift. Higgins could also be seen in the pre-show video for the Epcot attraction Test Track. However, the ride was refurbished in 2012 and the pre-show room was removed.
Higgins directs and appears on the stage from time to time as well. In 2004, he played Secretary of Defense Donald Rumsfeld in the American premiere of David Hare's Stuff Happens at the Mark Taper Forum in Los Angeles. In 2003, he played the title role in A. R. Gurney's Big Bill at New York's Lincoln Center Theater.
Higgins has been featured in TV ads for DirecTV alongside fellow Christopher Guest co-star Ed Begley, Jr. and for Old Navy. He also stars in season 2 of TNT's Raising the Bar as an openly gay, rule-obsessed judge. Higgins took part in The Suite Life on Deck, taking the role as the obnoxious and secluded Mr. Tipton.
In 2011, Higgins was cast in Happily Divorced opposite Fran Drescher. He played Fran's gay ex-husband, Peter Lovett, a character based on Drescher's real-life gay ex-husband Peter Marc Jacobson.
In 2012, Higgins was cast in The Legend of Korra as the voice of vain and eccentric business man Iknik Blackstone Varrick.