WASHINGTON — The Supreme Court heard arguments on Tuesday in a knotty environmental case over how to hold states responsible for air pollution that drifts across their borders and causes harm in downwind states.

If there was consensus among the justices, it concerned only the complexity and difficulty of the issues before them.

“This is a tough problem,” Justice Stephen G. Breyer said. A few minutes later, Justice Elena Kagan offered a similar assessment. “This is a hard problem,” she said.

Still, the questioning suggested that there may well be five votes to sustain the Environmental Protection Agency regulations at issue. “It’s certainly hard,” Chief Justice John G. Roberts Jr. said of the task of allocating responsibility, “but it is what the statute says, and it seems to me that if E.P.A. had taken a different view, it would have been contrary to the statute.”