As I cited before, Harvard's Martin Feldstein laid this out about a month ago...
Kevin Hassett provides some additional analysis showing that allowing offshore drilling will affect prices in the short term because of changed expectations:
The economics of natural resources clearly favors the Republican view.
The economics of extracting resources is quite simple and intuitive. If you own property that has oil in the ground, then you have to decide how rapidly you wish to deplete your resource. If prices are low today, and you expect them to be much higher in the future, then you will hold off pumping a lot.
Open Spigot Now
If prices are high today and are expected to be much lower tomorrow, then you would rather open up the spigot now when profits will be higher.
If exploration can be expected to be successful and significantly increase oil production in the future, then it would cause producers to revise downward their estimates for future prices. This would increase the attractiveness of extracting more today. As producers respond with higher production, prices today would drop.