“If you add all the numbers up, we can probably comply with the terms of the rule with very little impact, if any, because everybody’s heading in that direction to begin with,” he said. “Anybody who’s actually looked at the subject understands coal is going to play a dramatically reduced role in our nation’s energy portfolio.”

In drafting its regulation, the E.P.A. endorsed a 23-page “white paper” that Kentucky’s energy department sent last year asking that states be given wide flexibility in reducing carbon. Rather than regulate emissions from every smokestack, the E.P.A. is giving states an overall target to meet — in Kentucky’s case, a reduction of 18 percent of carbon pollution by 2030. The target is lower than for many states, taking into account Kentucky’s heavy coal habit, which accounts for 93 percent of its electricity.

The state has great flexibility in devising a plan to reach the goal. It can include switching plants from coal to natural gas, developing renewable energy like solar, and encouraging the use of efficient home appliances and insulation to reduce demand. And none of it will happen immediately: Any shutdowns are years away, as the E.P.A.’s proposal faces a political and legal onslaught.

But it is clear that if the plan goes into effect, there will be short-term disruptions, including to local economies tied to individual coal plants that might close, and in mining regions like eastern Kentucky, where the number of coal jobs is already at a historic low. The E.P.A. estimated that coal production in central Appalachia would fall by up to 37 percent as a result of its proposal.

“It’s going to be devastating if the power plant goes down,” said Dionna Sizemore of Burgin, a mother of two, ages 11 and 16, who moved from Harlan County, the heart of Appalachian coal country, to escape dead-end prospects there. “We know the impact it’s having on friends and family back home: people having to move off.”

Mr. Lyons said it was impossible to say this early which of the state’s 56 coal-fired generating units, if any, might close. Many have already installed costly upgrades to comply with earlier pollution rules.