Demagoguing on drilling for oil

I was just listening to a Democratic operative on Fox News. The way that he was defending the ban on drilling offshore and in ANWR was to say that the "oil companies" already had leases on a large amount of land that has a large amount of oil that is untapped. Why do they need more land to drill on when they have enough now? Someone needs an effective answer to those tactics, because there are many people, including in my family, who are "environmentally conscious", and who blindly support the drilling bans. By the way, an online poll at KRLD radio's website shows that 79% of respondents support lifting the ban on offshore drilling. That tells me that the Democrat demagogues have some work to do to make their position stick.