According to a new Quinnipiac poll, 51 percent of New York City voters disapproved of the ban, compared to 46 percent who supported it.
Republicans and blacks are particularly opposed to the ban, with 65 percent and 60 percent respectively saying they are unhappy with the law.
Women and white voters are more closely divided: slightly more women, 49 percent to 48 percent, oppose the ban, while slightly more whites support it, 49 percent to 48 percent.
Democrats are the only group asked giving Bloomberg's law any sizable support, 52 percent to 46 percent.
The law, intended to improve health and reduce obesity, is least popular in Staten Island (67 percent oppose) and the Bronx (60 percent oppose).
Starting in two weeks, restaurants, movie theaters, food carts and other vendors regulated by the city health department will stop selling soda and sweetened beverages in containers larger than 16 ounces.
Far more popular, however, is a proposed ban on plastic-foam containers meant to reduce waste in landfills. All groups surveyed, except Republicans, supported the idea with an overall approval of 69 percent to 26 percent.