Here are the numbers (ANWR, OCS), and a touch of analysis:
(click the image for larger view)
Drilling for more oil does NOT offer a path to "energy independence".
US Annual demand for oil is about 7,300 million barrels of oil. Subtract domestic production (1,825), and you've got about 5,100 of unmet demand (mostly, imports). ANWR and the OCS offer about 28,400 millions of barrels, TOTAL, so 28,400/5,100 gives 5.2 YEARS of energy independence, not accounting for increasing demand.
Another way of looking at it: independence from OPEC. That's easy - ANWR + OCS is about 28,400 millions of barrels of oil, and we import about 2,153 yearly from OPEC. 28,400/2,153 gives 13.2 years of independence from OPEC - again, not accounting for increasing demand.