"This has gone too far," a frustrated Mayor Bill de Blasio said this week. "It's time to take some real steps to regulate this reality."
But that could be easier said than done. Legal experts say proposals for a city law to rein in the characters - possibly by requiring licenses and background checks - could violate free-speech rights.
At issue, they say, is whether the characters can be considered a form of street performance, protected by the First Amendment, or a form of commercial activity subject to regulation.
It's a distinction that varies from character to character, and comes down to whether they merely hope for tips or demand money, which some tourists have complained is often accompanied by hounding and harassment.
"If you can prove that they are there to seek money, not simply conveying a message ... they are subject to greater regulation," said University of California constitutional law professor Jesse Choper.
George Washington University constitutional law professor Jonathan Turley agreed but said any such regulation must be written carefully to avoid selective or arbitrary enforcement. Singling out just those who wear costumes, for example, could be problematic.
"People are physically assaulted every day in New York City, whether they're costumed characters or in business suits or in bathing suits. And when politicians call for regulating someone in a costume, it's clearly inane," Turley said. "You have people on Wall Street who violate the law, and we don't subject people in Armani suits to special regulations."
City Council members Dan Garodnick and Andy King have drafted similar proposals requiring licensing and background checks, though King's would also require that costumed performers wear a picture ID.
De Blasio spokeswoman Marti Adams said the administration is currently reviewing the potential legislative remedies, adding: "It is well settled that even with respect to activity otherwise protected by the First Amendment, the city can enact laws designed to protect public safety."
For months, there have been headlines about pop-culture characters allegedly assaulting tourists in disputes over money. A Cookie Monster was accused of shoving a 2-year-old. An Elmo was accused of berating tourists with anti-Semitic slurs.
There also have been recent reports of a brawl between two Statues of Liberty, and a man dressed as Woody from "Toy Story" groping women.
Last Saturday, a man dressed as Spider-Man was arrested on charges he slugged a police officer who tried to intervene during a dispute with a woman who offered $1. Authorities say the crime-fighting hero told the woman he only accepts $5, $10 or $20.
New York's regulation push is backed by the nonprofit business group, the Times Square Alliance, which on a recent night counted no less than 76 costumed characters prowling the square, and the Broadway League, which blames the aggressive characters for a downturn in theater business.
On a sunny afternoon, Times Square was filled with about two dozen characters, including multiple Elmos, a Minnie Mouse, a Hello Kitty and more than one copper-green-skinned Statue of Liberty. At least two characters - Minion from "Despicable Me" and one Elmo - said they purchased their knockoff costumes, made in Peru, for about $300.
Speaking in Spanish through their masks, several people acknowledged they are living in the U.S. illegally and said they rely on Times Square tips to feed their families. City officials acknowledged that some of the characters are in the country without legal permission but said they don't know how many.
Pablo Fuentes, 40, an unemployed construction worker with four children from Paterson, New Jersey, said he works five days a week as Minion, earning about $55 for each six-hour shift.
"A license would be good for everybody, for the customer, for us, for you," he said. "This is a job, and we're not doing something wrong. Everybody needs a job."