Obviously, America would be in trouble. We'd have to subsist off of what we have stockpiled and what we can drill for domestically. But the government has planned ahead. Following the energy crisis of the 1970s, the U.S. Department of Energy started storing oil in the Strategic Petroleum Reserve (SPR), a network of salt-dome caverns located around the Gulf of Mexico. The Reserve is meant to safeguard against a major shortage, and it currently holds more than 700 million barrels of crude oil.
That may sound like a lot, but we go through the stuff pretty quickly. The United States currently consumes more than 20 million barrels a day—more than any other country in the world. Factoring in the 5 million barrels a day that we currently produce at home, the Department of Energy estimates that the SPR could support America for 58 days.
All told, including offshore oil, there are at least 23 billion barrels of oil under U.S. territory (that we know of). Even if the United States could somehow get its hands on all of that oil in one fell swoop, and add that to the 700 million barrels in the SPR, we could only sustain our current rate of consumption for about three years before running dry.