I'm pretty sure the following is an okay cross-section of the offshore drilling debate:
Here and here (News and Observer), here and here (Washington Post)
Much of the current discussion tying offshore drilling to the cost of gas is erroneous. Media outlets regularly cite polls that claim large numbers of Americans support offshore drilling. Those same polls, however, see a plummet in support whenever they include the (correct) disclaimer that offshore drilling will not affect prices at the pump, now or in the immediate future.
Should the federal moratorium be lifted, fuel prices won't drop for several years, and when that day finally comes, at best (and this is tenuous) there will be a per gallon savings of roughly a few cents (3.99/gallon vs 3.96/gallon).
What's more, the international market determines oil prices (for a primer on how and why, read this). With booming economies in China and India, the price of oil will not lessen as industrial and personal demand skyrockets across the world. Only a serious commitment to renewable energy will bring energy costs under control. A clean energy initiative will create new jobs and make us more energy independent and flexible in times of economic duress.