As the national average gasoline price climbs steadily toward the $4 mark, calls to increase domestic drilling in the United States have grown louder. Drill hawks would like to see the administration open up new areas like the Alaskan National Wildlife Refuge and Atlantic Continental Shelf to oil and gas drilling, and update laws and regulations to encourage development of unprotected but still-unused sites throughout the country. Likely feeling the pressure, president Barack Obama pledged this month to reduce the nation’s dependence on foreign oil by one-third within the next decade—largely by stepping up domestic production.

But while “drill baby, drill,” continues to be a popular refrain for administration critics and some Democrats hailing from oil-producing states, the argument’s relevance to gas prices has recently come under greater scrutiny. A growing consensus of energy experts and analysts have lately come out against the idea that increasing the balance of domestically produced energy could yield significant relief to consumers struggling with high pump prices.

“This drill, drill, drill thing is tired,” said Tom Kloza, AAA’s chief oil analyst responsible for calculating gas prices, to CNN Money. “It’s a simplistic way of looking for a solution that doesn’t exist.”

As the CNN article points out—and as we’ve pointed out here several times in the past—the interconnected nature of global energy markets means that while any increase in oil production technically results downward pressure on world prices, the effect of increasing domestic production wouldn’t be so much to lower prices in the United States, but to lower prices everywhere—meaning that American consumers would feel only a small fraction of the theoretical relief.

But since OPEC and other major producers tend to tie export levels to price, the reaction to more American oil on the market would likely mean cuts in production in places like Saudi Arabia, Kuwait, and Venezuela. The net result? A barely-significant increase in the amount of oil available for purchase and little to no difference in the price of gas at the pump.

Then there’s the matter of how long it will actually take to get the currently off-limits oil. The EIA estimates that it would be ten years (after congressional approval) before the first barrel of oil produced at ANWR hits the market, and peak production from offshore sites would reach just 500,000 extra barrels per day by 2030. While that would be a relatively significant increase in daily U.S. production—which currently hovers slightly below 10 million barrels per day—the impact that those new offshore areas would have on U.S. gas prices would likely be just a few pennies per gallon.

For drivers hurting from expensive gas, the choice is clear: Either wait years for the political dust settle and domestic production to expand—all in the service of saving a few cents per gallon—or find a more fuel-efficient car that could cut your monthly fuel budget by 20 percent, 50 percent, or even higher.