I hear this bit of disinformation hourly on NPR, and even on Fox. It isn't true. Obama could resume permitting drilling in the Gulf of Mexico. He could OK the Keystone XL pipeline. He could lease oil sands in Colorado. He could issue off shore leases for the Atlantic coast and the Pacific coast. He could start drilling in the "Alaska National Wildlife Refuge" a bit of frozen tundra on the shore of the Arctic Ocean. He could scrap the boutique gasoline blending rules which prevent selling gasoline across state lines. He could stop closing gasoline refineries in the Caribbean.
Drilling does lower prices. The price of natural gas dropped from $12 a thousand cubic feet in 2008 to $3 today. That's a 75% reduction in price in just four years. All done by drilling.
And the price reductions come even faster. Oil and gasoline are traded on commodities markets world wide. Those markets are future oriented. Prices are set by trader's expectations of the price in the future. If suppliers expect to get better prices next year, they don't sell, they wait for next year. If buyers expect to higher prices next year, they will pay more this year to avoid getting ripped off next year. If the markets were convinced that the Americans were serious about increasing production, prices would fall. It would only take a few months for the markets to decide the Americans were serious.