The seemingly endless stream of fliers, coupons, and menus stacked on front stoops and stashed in corners of apartment buildings would be a thing of the past in New York under a bill that would allow residents to bar distributors from dumping unwanted advertisements.

By posting a small sign or sticker stating: “This property does not want to receive unsolicited printed material,” a daily scourge for many New Yorkers would quietly come to a close.

“This is a first step in making sure that homeowners can do whatever they have to do without being bothered with circulars, and fliers, and all kind of junk they don’t want,” a Council Member Simcha Felder of Brooklyn said after hurling a heap of fliers and circulars on the steps of City Hall to illustrate the way front stoops appear to many New Yorkers arriving home from work.

The fliers are unsightly, occasionally lead to tickets from the Department of Sanitation (citing dirty sidewalks), and could prompt burglaries, as residents on vacation have no way to stop the papers from piling up, signaling no one is home, he said.

Mr. Felder’s bill does not explain how the law would be enforced or how offenders would be penalized. He said distributors would be held accountable for ignoring posted signs, and suggested they be fined at least $100 for each home or apartment building given unwanted fliers.

A spokeswoman for the Direct Marketing Association, Stephanie Hendricks, said local businesses often rely on fliers or menus to introduce themselves to a new neighborhood. She said she thinks a balance can be found that doesn’t harm small businesses.

Past efforts to stamp out the unwanted fliers have languished at City Hall, ultimately going nowhere because they were believed to violate the First Amendment.

An associate professor of culture and communications at New York University, Siva Vaidhyanathan, said Mr. Felder’s bill is problematic because it does not exempt political literature from the voluntary ban.

“There’s nothing about the First Amendment that ensures restaurant menus get to you,” he said. “It is not about menus, and it’s not about ads for limo services, it really is about political speech.”

Mr. Felder said he doesn’t want an exemption for political materials. He said most political literature is sent through the mail and contributes to only a fraction of the paper build-up.

Mr. Vaidhyanathan said a case could be made that the legislation would favor wealthier politicians over newcomers who can’t afford to send campaign material through the mail and rely on volunteers to go door to door, dropping leaflets and fliers.

If the bill contained an exemption for political materials, he said, “it would be a much more reasonable policy.”