(Reuters) - Major food and seed companies appear to be on the verge of defeating a California ballot initiative that, if passed on Tuesday, would create the first labeling requirement for genetically modified foods in the United States.

In a campaign reminiscent of this summer's successful fight against a proposed tobacco tax in California, opposition funded by Monsanto Co, DuPont, PepsiCo Inc and others unleashed waves of TV and radio advertisements against Proposition 37 and managed to turn the tide of public opinion.

Four weeks ago, the labeling initiative was supported by more than two-thirds of Californians who said they intended to vote on November 6, according to a poll from the California Business Roundtable and Pepperdine University's School of Public Policy. On Tuesday, their latest poll showed support had plummeted to 39 percent, while opposition had surged to almost 51 percent.

The swing in sentiment in the final weeks was predicted by pollsters, based on the power of a $46 million "No on 37" campaign, one of the best-funded for a California ballot measure fight. The ads claim the "badly written" initiative would increase the average family's grocery bills by $400 annually and hobble California farmers. Opponents also take aim at what they call "special interest exemptions" for restaurant food and products from animals fed with grain containing genetically modified organisms, popularly known as GMOs.

Backers of the labeling initiative say consumers have the right to know what is in the food they eat. They dispute opponents' cost projections and say labeling would not be burdensome to families or businesses.

They could still prevail on Tuesday if the polling turns out to be wrong, or if a last minute push by grassroots supporters takes root.

Many processed foods sold in the United States are made at least in part with corn, soybeans or other crops that have been genetically modified - crossed with DNA from other species to do things like make them resistant to insects or weed killer.

Each side accuses the other of resorting to desperate measures to mislead voters and using science that falls short of rigorous standards.

Such polarized debate is common in California, where ballot measures play a big role in governing. But labeling proponents say it also speaks to the research gap around GMOs, specifically a lack of mandated government studies that would show whether long-term consumption of GMOs causes health problems.

The U.S. Food and Drug Administration has determined labels are not needed for GM crops that are "substantially equivalent" to non-GM crops. The United States does not require labeling or mandatory independent pre-market safety testing for GMOs. At least three dozen countries require labeling and mandatory pre-market safety testing, said Michael Hansen, senior scientist from watchdog group Consumer Reports.

Some food and agriculture experts predict food companies would remove genetically modified ingredients rather than label them just for California - a move that would hit the multi-billion genetically modified seed business, where Monsanto and DuPont are market leaders.

Monsanto, the largest backer of the campaign with more than $8 million in funding, and DuPont say Proposition 37 would mislead consumers. PepsiCo referred reporters to the "No on 37" campaign.

TARGETING FLAWS IN INITIATIVE

Consumer advocates say the "No on 37" campaign has employed many of the same tactics the tobacco industry used this summer in California in a $47 million campaign that defeated Proposition 29, which would have raised cigarette taxes by $1 per pack to fund cancer research and other health efforts.

Opponents of the tobacco tax overcame early support approaching 70 percent by flooding airwaves with ads, including one featuring a doctor in a white coat warning that tobacco tax proceeds would not be spent on cancer treatment and could be shipped out of state. Outgunned supporters said those claims were false.

The food and tobacco industry campaigns both employed messages that weren't "arguing with the premise of the initiatives, but rather making picky criticisms of the details of the initiatives," said anti-smoking activist Stanton Glantz, a professor and researcher at the University of California-San Francisco.

"No on 37" spokeswoman Kathy Fairbanks rejects the notion of copycat tactics and said the similarities between the two campaigns are limited to pointing out flaws in the initiatives and spending significant money on ads.

Backers of Proposition 37, including thousands of individual donors, organic food companies and natural health news provider Joseph Mercola, have been outspent roughly six to one, according to campaign reports filed with the California Secretary of State. In their final push, they are trying to trumpet cases where they say opponents have used misinformation to sway the public.

MISSTEPS ON BOTH SIDES

Both sides have made missteps.

Supporters of Proposition 37 got a boost when the Academy of Nutrition and Dietetics said "No on 37" inaccurately stated in the California official voter information guide that the academy had concluded that GMOs were safe.

"We are concerned that California's voters are being misled to believe the nation's largest organization of food and nutrition professionals is against Proposition 37, when in fact, the academy does not have a position on the issue," its president said in a statement in early October.

"No on 37" said it based its information on a policy statement on the academy's website and that it was not aware the position had expired in 2010.

The FDA also set the record straight on a "No on 37" mailer that put the FDA's logo below a quote criticizing efforts like the California labeling measure as "inherently misleading." The use of the quote next to the logo made it appear that FDA had weighed in on the fight.

FDA spokeswoman Morgan Liscinsky said the agency made no such statement and had no position on the initiative. "Yes on 37" also asked the U.S. Department of Justice to investigate the allegedly fraudulent misuse of FDA's seal in that mailer - something that won't be resolved until well after the election.

Then, just four days before the vote, supporters of Proposition 37 fumbled the facts about the status of its DOJ request, releasing a statement titled: "FBI opens investigation into No on 37 shenanigans."

The U.S. Attorney for the Eastern District of California quickly responded: "Neither the FBI nor this office has a pending investigation related to this matter."