I'll get to the numbers in below, but let's think about his logic. The point he's trying to make is that, if only the environmentalists and regulators would get out of the way, we could produce our way to lower energy prices. Again, I'm not going to address the fact that crude is a world market and whether OPEC would reduce production to offset our increase. But we currently import about 13.6M barrels of oil per day and produce about 5.5M barrels per day. So, if we doubled our output, something no sane individual contends we could do in any kind of short time span, we'd still import over 40% of our oil. Keep in mind that the producers of oil in the US will sell into a world market - it's not as if they'll sell it cheap here.
Now, on to the numbers. Santorum states that, at "current rate of extraction" we have 263 years worth of proven reserves in the US. At the EIA (U.S. Energy Information Administration) we find that, in 2010 the U.S. "produced" 5.512M bbl/day. Thus, Mr. Santorum is claiming that U.S. proven reserves are (365.25*263*5.512M) 529 billion barrels. But at this EIA page the U.S. proven reserves are stated to be 20.6 billion barrels - about 3.9% of Santorum's number. Houston, we have a problem.
What could explain this discrepancy? To start, I can imagine that he might include the so-called "oil shale" in CO, among other states. According to this Wikipedia article (I've cross checked with some other sources), there may be about 1.9 trillion barrels of "shale oil" reserves (oil derived from the kerogen in shale formations as distinguished from "tight oil" which is conventional crude trapped in shale formations). If this is what Santorum is referring to, current extraction would deplete this plus the conventional reserves shown previously in 954 years. A more conservative estimate by the RAND Corporation is that 800 billion barrels of shale oil may be technically (not to say economically) recoverable.
I was able to find an article that I believe to be what Santorum was trying to quote, it's by Daniel Horowitz in the Redstate.com web site. Pulling figures from this report by the Congressional ResearchService, Mr. Horowitz states the following:
Parenthetically, the cessation of Libya’s mere 1.7 million barrels of production per day has caused chaos in the global market. Were we to pump our oil reserves at a similar rate, the oil would last for 263 years. This would presumably have a commensurately positive effect on oil prices.The "263 years" figure seems unlikely to be a coincidence. What Horowitz did was divide the 163 billion barrels that are "proved" plus "undiscovered technically recoverable" in the Congressional Research Service report and divide by 1.7 million barrels per day times 365.25 days per year. I suppose his point was that, were we to go after these reserves, we'd eliminate the market turmoil caused by issues in unstable producers. How Santorum got from there to "we have 263 years worth" is a reflection either of his willingness to baffle his audience with... bull puckey or his inability (or that of his staff, who no doubt gave him the talking point) to interpret reports.