When President Obama announced strong measures to combat climate change last week, environmentalists who felt he had long soft-pedaled the issue for political reasons rejoiced.

But many Republicans were just as gleeful — in the belief they had been handed a powerful issue to use against Democrats in the 2014 midterm elections in energy-rich states from Texas to Minnesota.

Elected officials and political analysts said the president’s crackdown on coal, the leading source of industrial greenhouse gases, could have consequences for Senate seats being vacated by retiring Democrats in West Virginia and South Dakota, for shaky Democratic incumbents like Mary L. Landrieu of energy-rich Louisiana, and for the Democratic challenger of Senator Mitch McConnell of Kentucky, the Republican leader.

In ordering limits for the first time on carbon dioxide emissions from up-and-running power plants, Mr. Obama jabbed that opponents belonged to “the Flat Earth Society.” But in coal country, it was Mr. Obama who was called out of touch, with predictions of job losses and spiking energy bills.