1. The US could pump all the oil it has control over and global demand is such as that would not keep pace with global supplies. Demand is growing at a rate you could not pump it fast enough to affect the global price. The notion of if only we would pump more oil, our gas prices would decrease is just plain wrong.
2. There is no home team advantage for having your own oil supply. The prices paid per barrel in Norway and Saudi Arabia are a global price. The only exception to this is where supplies cannot make it to the market creating a temporary excess local supply. For example, Tulsa, OK enjoyed a brief cost at the pump advantage because of a temporary glut due to a pipeline issue preventing transportation to the US gulf coast.
3. The government cannot dictate prices. If you are operating in a market and the government attempts to set a price less than the market can support either by direct price fixing or taxation policy, supplies will diminish creating a shortage. Ask Jimmy Carter about his 'windfall tax' policy and gas lines. At best, the government can help reduce demand by advocating alternatives. For example, a natural gas powered municipal power plant that charges a car during off peak hours reduce global demand and global dependence.
4. It is true that gas prices were cheaper in 2008. That is because demand slumped world wide. People drove less. People bought less. People used less energy.
5. Certain policies seemingly intent on reducing the foreign demand for oil actually increase it. For example, considering the US gulf coast is quite capable of growing more efficient sugar cane, corn based ethanol mandates not only increase the cost of the numerous food supplies that rely on corn, but also increase demand for the oil it is intending to replace in uses such as fertilizer, diesel fuel, and the direct production of ethanol itself.