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I find extremely suspicious that all the pro drilling politicians can not trot out one reputable economist to make a prediction about how much ANWR and offshore drilling will decrease gas prices. An increase in domestic production probably will not have a great impact on gas prices. Recently gas price increases suggest that world-wide demand is relatively inelastic and growing. Any small price reduction may just mean higher consumption and thus little price impact.
The other crucial variable is that the majority of the world's oil reserves are controlled by foreign state run oil companies that can always reduce production either in concert or in the case of a big player, like Saudi Arabia, alone to maintain a particular price target.