But people who study oil markets for a living say they are wrong.
"I would really doubt that that [2008 price drop] would have been because we committed to more drilling," said Phyllis Martin, an analyst with the U.S. Energy Information Administration (EIA), which just released its detailed, annual outlook on energy supply and prices.
"It was most likely the recession," Martin explained. "When demand cuts back, the production cuts back and the prices fall."
As for opening four new drilling leases, that's not even a drop in the bucket.
Analyst Lynch said that, if the nation took an extremely vigorous stance on oil exploitation -- and relaxed restrictions on the Gulf and drilled in the Arctic National Wildlife Refuge in Alaska and off the coast of California, where America's most easily accessible offshore oil is located -- it still would not have much of an impact.
"With the exception of the deep Gulf, where there are restrictions, people are drilling as fast as they can," said Lynch, who regards himself as a moderate Republican. He is bearish on oil prices and believes the cost of crude will drop soon, regardless of an government policies.
"You might, under really optimistic scenarios, over five or six years, add 2 million barrels a day of production," said Lynch, who favors more drilling, even if he rejects the politicians' arguments. "On a global scale, it's significant. But we would still be big importers -- we would still be dependent on foreign oil."
And prices would not move much because of it, the analysts explained. Oil is traded on a world market, and the United States does not have enough petroleum to increase the global supply, which would reduce demand -- and thus the price -- for fuel.
"In 2009, the U.S. produced about 7 percent of what was produced in the entire world, so increasing the oil production in the U.S. is not going to make much of a difference in world markets and world prices," said the EIA's Martin. "It just gets lost. It's not that much."
And boosting drilling in the outer continental shelf?
"What comes out of the OCS is about 1 percent of the world total, and that's not enough to affect world prices," Martin said, even noting that she believes there are even more untapped reserves than officials can estimate at the moment.
But we could also create jobs by having people dig holes and then fill them up again. Or by hiring all the out-of-work construction workers to install solar panels on the roofs of every government building, which would probably have a greater effect on energy prices than drilling.