More: Concerns about the results of judge shopping by conservatives are not confined to Democratic Party politicians. The direction of cases to single-judge districts, like the one headed by Kacsmaryk, has produced such poorly reasoned decisions that the conservative Supreme Court has repeatedly turned them back.

The high court's patience may be running thin, too. During arguments over the availability of the abortion drug mifepristone, a ruling that originated in Kacsmaryk's courthouse, the justices seemed exasperated at how such a poorly structured case, with no clear claim that the anti-abortion plaintiffs had standing to sue, made it all the way to them. At one point, Justice Neil Gorsuch, a conservative Trump appointee, bemoaned the manner in which the case came before the court.

"We've had, one might call, a rash of universal injunctions or vacaturs," Gorsuch said, describing the type of cases sought by judge-shoppers. "This case seems like a prime example of turning what could be a small lawsuit into a nationwide legislative assembly on an FDA rule or any other federal government action."

Godbey may be able to ignore Schumer's entreaties for now, but continued irritation from the Supreme Court's conservatives could be more persuasive.