Disney’s Academy Awards push for “Toy Story 3” might hit a PR roadblock thanks to an anti-Oscar campaign by union hotel employees at the Disneyland Resort in Anaheim.

On Monday evening, members of the Unite Here union held an informational picket outside Disney Studios to coincide with a “Toy Story 3” screening for members of the Academy of Motion Picture Arts & Sciences. They plan to tote placards reading “Don’t Vote for Disney,” according to Unite Here spokeswoman Leigh Shelton.

The union’s also launching a website, Notoystory3.org, and plans to picket other “Toy Story 3” screenings.

Unite Here asserts that the long-running dispute with Disney centers on the company’s demand that the employees change to a “Disney Signature” health care benefit plan requiring workers to pay premiums that would be “unaffordable” for many of the employees — most of whom don’t currently have to pay for health care coverage.

The Unite Here employees in the dispute have been working under an expired contract for nearly three years. In February, the union staged a hunger strike — with workers sleeping in tents on sidewalks — outside the Grand Californian Hotel in Anaheim and outside Disney corporate headquarters in Burbank.

“This is just another publicity stunt from (Unite Here) leadership to distract from the fact that after nearly three years their members are still without a contract,” said a Disneyland Resort spokesman. “We have offered a fair and comprehensive contract, including annual wage increases, paid sick leave and reliable, affordable health care.”

Under the proposed plan, Unite Here asserts that a family of four would have to pay $365 a month, and that figure would rise to $535 a month over the following five years. Disney disputes the accuracy of those figures.

Shelton said some of the employees — who include bellmen, room attendants, cooks and dishwashers — are currently receiving less than $9 an hour.

“Over the years, worker have foregone significant wage raises in order to maintain quality affordable health care,” Shelton said. “We’ve done loads of public events about this issue, and people in Hollywood are usually very sympathetic and ask what they can do to help. We’re targeting ‘Toy Story 3’ because there are a lot of union people in the industry.”

Unite Here has already shown significant clout among the Hollywood unions, as the Directors Guild of America and the Writers Guild of America both decided recently to move their awards shows from the Century Plaza due to a Unite Here dispute with Hyatt management over the issue of organizing workers at nonunion hotels.

“Toy Story 3” has grossed more than $1 billion worldwide, is on the shortlist for the animated Oscar and has a strong shot at earning one of the 10 best picture nominee slots. Disney’s launched an ad campaign featuring “Toy Story 3” characters linked to images from best picture Oscar winners of the past.