His promise is that (blocking the Lieberman-Warner climate bill and) opening up drilling off the coasts, in the Gulf of Mexico, in northern Alaska, and in the Rockies (for oil shale) would lower gas prices.
Now, for one thing that's just a lie. It's false. According to the EIA, the U.S. has about 21 billion gallons in proven oil reserves -- about 3% of the world's total. Even if we started drilling today, it would be 10 years before we got substantial production out of those fields, and 20 years before peak production. Ten years -- while gas prices have risen $0.50 just this Spring.
Right now, Saudi Arabia is sitting pretty, enjoying sky-high oil prices. They are ignoring our entreaties to pump more because they like these supply constraints just fine (and they probably can't pump any faster if they wanted to). Say we start pumping those reserves out into the world oil market. What's to stop Saudi Arabia from dialing back production a little bit, so supply (and prices) stay roughly the same? Answer: nothing. U.S. domestic oil prices rise to meet world prices, and those prices are outside our control.
In short: The U.S. cannot affect oil or gasoline prices in any significant way by drilling more oil. Full stop. Gingrich is knowingly lying to people (and taking their money).
The other thing I'd say about this is that the We campaign people and all the other earnest politicians and enviros out there trying to convince us that climate and energy are bipartisan issues should wait until they are actually bipartisan before celebrating. Gingrich is using a green fig leaf to push the same corporate-friendly policies the GOP has been pushing for decades, and rather than getting smacked down, he's being helped by greens. It's stupid.
Here's the man himself, delivering his oily lies just like those of us alive in the mid-'90s remember: