The GMB said a survey of 1,000 people it commissioned showed that almost two out of five said they would be less likely to shop at Asda after hearing the terms of the new contract.
The union has been embroiled in a long-running dispute with Asda over the new contracts, which it says removes paid breaks and changes shift patterns.
A total of 17 percent said they would be more likely to shop at Asda, with 43 percent saying it was neither more or less likely.
Asda says most of its employees have signed the new contract, adding that basic pay will increase, while workers will receive an enhanced package including an annual bonus.
National officer for the GMB Gary Carter said: "Asda used to be rooted in family values, this polling shows that's what Asda shoppers expect.
"Asda customers overwhelmingly want to be served by people who are respected and treated well in their jobs - no one wants to feel bad about doing their shopping, especially at Christmas.
"GMB don't take any joy from this, because our members' jobs depend on people shopping at Asda but people want to feel good about where they shop and clearly could vote with their feet.
"Asda could still rethink their plans and simply stop going down this route of imposing punishing new terms on loyal workers who work hard for them every day. GMB is calling on them to do just that."
An Asda spokesman said. "We have always been clear that we understand people have responsibilities outside of work and we will always help them to balance these with their work life.
"We will not be asking them to constantly move the time they work, their days or departments."