A few thoughts based on some numbers I dug around for:
The US, according to this site, uses 20.7 million barrels of oil a day. Annually, that translates to 7.35 billion barrels of oil (BBO). Estimated proven reserves (excluding the Strategic Petroleum Reserves) is 21 BBO; including SPR is 21.7 BBO. This is oil that, as I understand it, is still in the ground but is believed to be recoverable under current technological and economic conditions (at least 90% certain) and is being drilled for. The 134 BBO Sam talks about is prospective - it’s essentially assumed to be there but there hasn’t been too much research or actual testing to back the assumption up. Among the latter category is the ANWR, with the second biggest estimated reserves at 26.6 BBO (after the Gulf of Mexico, estimated at 44.9 BBO).
Now, if all that oil were already drilled up, packed and ready to go, we would indeed be all set for quite a while. But it’s not. It’s still in the ground. And we can’t get it up all at once. If the ANWR were to go online today, its estimated output (between 2018, when the first well comes online, and 2030) would be 4.3 BBO (out of a total 10.4 BBO estimated), averaging about 358 million barrels annually (although the numbers are a lot less than that to begin with - see page 5 of this report. To keep up with current demand, we’d need 20 oilfields of that caliber. Which the US doesn’t have - total domestic crude oil production for 2007 was only 1.85 BBO. No matter how you slice it, energy independence based solely on increased oil drilling is an absolute myth.
One other aspect of pulling oil from the ground is of interest here: the concept of “economically recoverable resources”. Essentially it’s the amount of oil recoverable from a given field as a function of the price of oil per barrel on the world market. (Analysis of this function regarding the oilfields in the four Offshore Coastal Shelf areas near the US are found here.) Unsurprisingly, the higher the price of oil per barrel, the greater amount of oil can be recovered from a particular field. So if the United States, for some reason, shut its doors and neither imported nor exported oil, the price of oil on the world market would still affect how much oil is recovered domestically. End consumers would still be screwed if the oil market collapsed. Even if the US oil industry completely decoupled itself from the world market, higher oil prices would still be in its best interest. The only way, under current conditions, for the US to increase its domestic oil supply is to increase the price of oil per barrel.
Depending on foreign oil imports isn’t going to help much in the long run, either. New discoveries of oil had dropped to 10 BBO annually by 2004 while consumption was approaching 30 BBO.
In short, we don’t even have enough to coast on for the next ten years while fields like the ANWR wait to come online; even if we did the amounts they put out would only slow the decline, not stop or reverse it.