The Energy Information Agency, the non-partisan agency within the Department of Energy which studies natural gas and petroleum supplies, says the impact would be about 1.6 percent on oil supply and that's decades from now.
"The projections in the OCS access case indicate that access to the Pacific, Atlantic, and eastern Gulf regions would not have a significant impact on domestic crude oil and natural gas production or prices before 2030," the study says. "Leasing would begin no sooner than 2012, and production would not be expected to start before 2017."
It's worth reading the whole study here if you really want to get wonked out on oil prices instead of listening to the hyped up rhetoric flying on Capitol Hill. The study was done in 2007, so it's possible the runup in oil prices over the past year would have an adjustment on some of these statistics, but the analysis on available oil resources is sound.
The EIA also did a helpful study on the Arctic National Wildlife Refuge oil reserves, showing that it would produce one million barrels a day, seven to 12 years from now. That's significant, but the United States consumes about 21 million barrels a day, so one million barrels a day a decade from now would knock about five percent off the price of oil.