To bottle up the movement to tax certain foods and drinks, major beverage companies like Coca-Cola and PepsiCo are spending millions of dollars on commercials that push people to vote to prohibit local governments from slapping levies on those goods, The New York Times reported on Saturday.

According to the report, voters in Washington and Oregon have been inundated with advertisements from groups like Yes! To Affordable Groceries, which have already spent more than $25 million on the campaign. These advocacy organizations are largely financed by the big beverage companies, the report noted, who are fighting anti-obesity efforts pushed by state and local governments.

Health advocates hope the tax on sugar-packed drinks will reduce consumption of them. They point to the fact that nearly 40 percent of Americans are obese, according to the Center for Disease Control. However, the beverage giants are pushing back by funding ballot measures and legislation that would block municipalities from imposing taxes on key goods and services, The Times noted.

Yet William M. Dermody Jr, a vice president with the American Beverage Association, an trade group, took issue with elements of The Times' story.

In an interview with CNBC, Dermody insisted the effort to reject food and beverage taxes was largely a grassroots effort being driven by a broad local coalition of citizens. While big companies like Coke and Pepsi were involved in beating back levies on food and drink, he insisted those efforts were not solely about sugary drinks.

"The beverage industry is standing with small business and consumers locally who want to keep their groceries affordable," Dermody said on Sunday – even as he acknowledged the industry had funneled "significant" resources into local efforts to push back on the levies.

Data provided to CNBC by the association showed the industry has contributed around $3 million in cash and in-kind contributions to initiatives in Oregon, and $20 million in the state of Washington.

"What this is about is people wanting to protect their groceries from excessive taxes," Dermody said. These are democratic [constituencies] and people are saying 'enough' to higher taxes"

More than 30 countries already tax sugary beverages. Municipalities across the U.S. are now considering doing the same, and sweet drinks are already pricier in seven cities, including Philadelphia, San Francisco and Boulder, Colo.

That beverage companies dislike the tax initiatives is perhaps unsurprising. A public health study found soda taxes in Berkeley, Calif. resulted in a more than 20 percent drop in soda consumption.

The full report can be found on The Times' website.