The Democrats want to take away tax breaks from the big oil companies, the Republicans want to let them drill more places. These may be good or bad policies, but neither will have any noticeable effect on the price of gas.
Let's say that 20,000 times. Neither of these policies will have a noticeable impact on the price of gas. This is not a disputable point.
Getting more tax revenue from the oil industry may be a good idea, especially in a context where Congress is obsessed with reducing the deficit, but it will not reduce the price of gas.
Similarly, the opening of new areas off the coast to drilling cannot possible generate enough additional oil to have any noticeable effect on the world price of oil. When politicians say that they want to increase drilling to bring down gas prices they either do not know what they are talking about or they are not being truthful.
Either way, this assertion should be treated as a gaffe. (You know, like then Senator Obama's comment about guns and religion during the presidential primaries.) Politicians who make such inaccurate assertions should be pressed on them. The media should try to determine whether they are really completely ignorant of the dynamics of the world oil market or they are just trying to deceive the public.
It should not just imply that opening new areas to drilling is a plausible way to reduce gas prices, as is done in this article.