The Washington Post printed an oped column from Alaska Senator Lisa Murkowski arguing for increased domestic oil production. The column directly confuses short-term economic weakness with the impact of long-term oil prices.
It cites Harvard professor and former AIG director Martin Feldstein as supporting the claim that "that if prices remain high, economic growth will languish." In fact, the quote from Feldstein explicitly refers to economic growth this year. There is nothing that the government can do that will in any significant way affect the amount of oil that the U.S. produces this year. Therefore, Feldstein's statement is irrelevant to the issue at hand.
As far as the longer term question, higher oil prices would have a modest impact in slowing growth in most economic forecasting models. However even large increases in domestic production would have little impact on world oil prices (the relevant variable) and therefore have little effect on economic growth. A serious newspaper would not have allowed a columnist to make such misleading assertions.