I believe w's energy department has stated ANWR oil will not lower the cost of gas and will have no serious impact on oil supplies. This is about profits - not helping US consumers.
Even if every drop of US oil is pumped it will be a drop in the bucket.

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A nation of slaves is always prepared to applaud the clemency of their master who, in the abuse of absolute power, does not proceed to the utmost extremes of injustice and oppression.
Edward Gibbon