The Republican lawmaker told reporters in Charleston on Friday he wants to write a bill to do both.
An energy industry group, the American Energy Alliance, is running radio ads in the state criticizing Graham's position on cap and trade carbon taxes. The ads say that approach will cost jobs.
Graham says none of the bills in the House or Senate now are good for business, but he says there has to be some sort of carbon control.
Graham says if carbon is not controlled, people will keep building coal plants. He says the nation needs to make it worthwhile to invest in wind, solar and nuclear power.
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