The plumbing merchant has been told the signs, which have been advertising the business for the past 20 years, are too big and may have to be pulled down.
Mr Wheeler, who set up the business in 1984, has branded the move "ridiculous and petty".
In a letter from Stafford Borough Council, seen by the Express & Star he has been told that his bigger signs need advertising consent or 'formal enforcement action' may be considered.
Mr Wheeler, who employs 13 people at the plumbing shop and bathroom showroom, said: "I just cannot understand why, after 20 years, these signs have suddenly become a problem. There are shops closing down in Stafford at a rate of around two a week and they're wasting their time doing this. It's uncalled for."
Mr Wheeler claimed it is an "attack on the small man. We have been here and employing people for years and this is the third recession we are coming through," he said. "We're here and doing okay and now we have to face the possible extra expense of this."
Since news of the possible enforcement action emerged, Mr Wheeler has been inundated with calls of support from customers and contacts.
A petition has now been set up in a bid to save the signs and customers have been going into the shop to sign it.
"I've been totally humbled by the support we have been given from local people," he added.
Mr Wheeler said he will now seek legal advice over the issue.
The shop and showroom are in a conservation area of the town, which means adverts cannot exceed a certain size.