The Hill reports that Republicans are trying to make an end run around Democrats and portray themselves as the environmentally friendly party. It's not entirely clear what this bold new plan entails--all the specifics the article mentions are either (a) worthy but modest ideas that Democrats support too, or (b) not actually good for the environment. For instance, according to the article, Republicans plan to abandon their emphasis on drilling in ANWR, and instead promote increased oil shale development. Large-scale oil shale production isn't feasible yet and would actually be significantly worse for the environment than drilling in ANWR.
It seems like the thing to do would be pick a message and stick with it: Either you're the party of cheap, dirty energy or you're the American version of David Cameron's Tories, but you can't be both at the same time. If you want to increase the supply of energy in order to lower the price, it doesn't take a Ph.D. in economics to realize that, regardless of what Lamar Alexander says, that will result in more energy being consumed, not less. Then again, given that the GOP nominee for president apparently doesn't understand his own cap-and-trade plan, it's hard to fault Republicans in Congress for having a hard time trying to come up with a coherent energy narrative.