Even before right-wing organizers backed away from their planned rally at Crissy Field, one group of counterprotesters had called off the dogs.

A suggestion that dog walkers foul up Crissy Field with large quantities of their pets’ droppings ahead of Saturday’s scheduled rally by the Patriot Prayer group quickly went viral this week. But a few hours before Patriot Prayer said it would hold a news conference across town instead, the man who dreamed the whole thing up, a San Francisco artist who goes by the alias of Tuffy Tuffington, surveyed the demonstration site and said never mind.

The problem: The site at the western side of Crissy Field had already been surrounded by a portable fence and no one — two-legged or four-legged — was getting inside.

That thwarted Tuffington’s hopes that his dogs Bob and Chuck could leave their mark, an idea he says he came up with while walking the pair in Golden Gate Park.

“Take your dog to Crissy Field and let them do their business and be sure not to clean it up!” he wrote in his online proposal, which spread faster than anything on the bottom of a shoe. Before long, about 1,000 dog owners said they were interested in participating.

Tuffington said he dropped by the site early Friday to check on the feasibility of going through with his vision, and decided it did not look possible. He also said he had “been getting quite a few threats” from people who didn’t think his idea qualified as fighting clean.

“I just had this image of people and dogs participating in civil disobedience,” Tuffington said.

He said he had planned to encourage participating dog owners to return to the site after the protest and pick up, or try to pick up, their pets’ handiwork. Thanks to the fence, and to Patriot Prayer’s plans to hold a press conference in Alamo Square Park instead of rallying in the Presidio, that will no longer be necessary.

Steve Rubenstein is a San Francisco Chronicle staff writer. Email: srubenstein@sfchronicle.com