Maxim,
I started reading your post and thought you had lost it. What a relief to find you were just stating Obama's position.
Actually, if Congress simply approved drilling in ANWR, the price of crude would drop, since the price is being "fueled" primarily by speculation right now. One analyst has stated an immediate expected drop in the range of $30-$50 a barrel(Sorry, I don't remember what news show I saw that on or who the commentator was). Opening up off-shore drilling would have a similar effect.
On the other hand, Obama's plan to spend money researching solar or wind (or gerbils on treadwheels, etc.) will cause an increase in gas prices, since he would fund it by increased taxes on the oil companies, which they would pass on to the consumer.