New York City certainly wouldn't be the first to impose restrictions. Dozens of West Coast cities, Washington, and Austin, Texas, have restrictions or full bans on plastic bags. (The City of Austin Resource Recovery department even has its own Pinterest page dedicated to DIY reusable bags.)
In California, about 120 cities and counties have adopted or are considering plastic bag restrictions, said Dave Heylen, spokesman for the California Grocers Association.
The hodgepodge of rules has led the California grocers to push for a statewide ban on all one-time-use plastic bags.
"Strictly from a business standpoint, we think our industry can regulate ourselves," Heylen said. "But in 2006, 2007, San Francisco came out with the first ban. ... Then other cities in California started to explore this, and we saw that a number of them were tweaking it a little bit. Maybe a higher charge here and there. Since our members do business in multiple municipalities, especially our bigger retailers, it made more sense from a business standpoint that we have one statewide ordinance."
(Read more: Sharing economy: Greater Depression in the making?)
At least one grocers group is against the New York plan.
"We're adamantly opposed to this," Brad Gerstman of the New York Association of Grocery Stores told Crain's New York Business. "It's a tax on small businesses and their customers, and it's insane at this juncture to further incentivize customers to go shopping in a different city or state."
Some stores are taking action on their own.
Nationwide chain Whole Foods Market eliminated plastic bags in 2008. It now offers 100-percent recycled paper bags for free or reusable ones for purchase. The stores also offer a five- or 10-cent credit for each bag a shopper brings in to reuse. It estimated that in the first two years it removed 100 million new disposable plastic bags from circulation, said company spokeswoman Libba Letton.
(Read more: Copper theft 'like an epidemic' sweeping US)
Ikea pulled plastic checkout bags from its 38 U.S. stores in October 2008. The company implemented a phaseout over a year and a half, and was at 92 percent of its elimination goal when the total ban went into effect. It sells an oversize, reusable blue bag for 59 cents.
The New York proposal seeks to build on a state law requiring large retailers to provide recycling bins for plastic bags. But that law has been poorly enforced and hasn't effectively cut the amount of trash, according to Alex Moore, the press representative for Councilman Brad Lander.
Proponents hope to pass the New York ban on free bags by the end of the year, Moore said.
—By CNBC's Amy Langfield. Follow her on Twitter @AmyLangfield.