the USA has some of the largest oil reserves in the world, and they just sit relatively untapped. ANWR is just one of them. we also have some of the world's largest reserves of coal oil. (sorry, meant oil shale)
basically, if the world decided to cut us off, it'd only be a few environmental policy changes and a few months of exploratory drilling before we're back in business...
and then we decide what to do with their oil reserves after killing whoever tried to cut us off.
We have more oil in oil shale than all other proven oil reserves on earth combined.
But, in the near term you would see fuel rationing with the majority of our domestic oil supply going to food production and the shipping and manufacture of vital supplies. All oil-burning power plants would be ordered shut down within the first couple days and there would be calls for people to severely curb their power consumption. Things like mowing your lawn with an electric or gasoline powered machine would be illegal. There would be a strong push for immediate public transportation systems to be put in place, like buses. Air traffic severely reduced, things like overnight shipping would be indefinitely suspended. Trains burning coal would be put back into production to help with some of the switch to a new energy policy. Oil shale would be extracted at a feverish pace to offset some of the demand. As a ripple effect, consumer goods would have to be produced domestically as it would be far too expensive to ship from overseas. Telecommuting and teleconferencing would become a normal aspect of daily life as companies attempt to adjust. Also, natural gas is used to replace heating oil in the north east.
In the long term, fast electric trains are used to link cities. Urban areas see a revitalization and massively grow in size. Driving becomes somewhat of a luxury because of the cost of either oil or lithium-ion batteries. The world would not be the same place. Countries in the Middle East that rely on oil sales become poor overnight. China, India, and most of the rest of the world for that matter have trouble feeding their citizens. International travel, outside of visiting close countries, means taking weeks off of work because the most affordable means of transportation would be on an Ocean Liner.
All this though, may be where we will be heading anyway as global oil demand surpasses easy oil production.