Another argument against this approach is that North American oil sources aren't as easily extracted as Middle Eastern sources. Part of the transition to North American sources includes developing better extraction technology as these sources start to be exploited. That requires real experience and years of R&D. If we just ignored our sources until we became 100% dependent on them, we're not going to be able to extract them quickly enough or efficiently enough. We've got to build up the technology and infrastructure before we become dependent.
But how does this help us? The oil market is international. If we wait until everyone else runs out of oil, then start drilling ourselves, we're still paying ultra-high prices for it.
Of course, unless you are suggesting we don't sell any of our own oil at that point. Sounds good in theory, until you realize that keeping oil product for domestic use (at say $100/bbl) leaves a lot of money on the table when you can sell it to another country for $400/bbl.
The oil market is international, but not immune from politics. The Saudis are currently willing to sell their oil to the US for a fair price. That isn't a situation that is guaranteed to continue, if the US digs up all their oil now they lose the future negotiating position of "screw you guys, we'll just dig up our own oil".