In a January 2014 violation notice, the agency said Mr. Johnson had violated the Clean Water Act by digging out Six Mile Creek and dumping in tons of river rocks without getting necessary federal permits. The agency ordered him to take steps to restore the creek under the supervision of environmental officials, or face accumulating fines of as much as $37,500 a day.

Mr. Johnson refused.

He argued that he had gotten full approvals from Wyoming officials, and said the federal government had no business using national water laws to make decisions about the creek that meanders through the family’s eight-acre property. Mr. Johnson and his wife, Katie, had spent $50,000 — most of their savings, they said — to create the pond to water their 10 head of cattle and four horses. Dismantling it now would be ruinously expensive and destroy what has become a tiny oasis for birds and wildlife, they said.

After more than a year of unsuccessful negotiations, the standoff veered into a federal courthouse last month when Mr. Johnson sued the E.P.A., asking a judge to declare his pond legal and wave away accumulating fines of as much as $16 million.

“They have no right to be here,” Mr. Johnson said. “We’re law-abiding people. It makes your blood boil that they would come after you like that.”