Not all that much oil actually... if you're counting only what's technically feasible and economically viable to extract. While neoconpoops, their brethren, Faux Noozies and Dittoheads will spout off about ANWR and environs being the magic answer to "500 years of American energy independence" (who do you wanna bet funded those studies?! 
) most reputable, non-partisan sources put the figure at something like 1-2% (at most) of the world supply. And before anyone gets all Palinesque about that, allow me to point out the reality that even if ANWR was drilled, it's not like that oil would be reserved solely for American consumers. Exxon and Co. are mutinationals and the markets for all resources are global... so quite a bit of that ANWR crude would likely end up in China, all things considered.
"Drill baby drill" only really means anything when you're talking about porn IMO.
And don't forget, there are different grades of crude oil.
The vertical axis is "API", which is a measure of thickness or density. The higher the API, the thinner/lighter the oil. The horizontal axis gives the sulfur content.
The Alberta tar sands are very close to the "Maya" grade. It takes a hell of a lot of nasty, toxic processing of the sludge to just get it thin enough to put into a pipeline, and then you have to do even more icky stuff to it to remove all the toxic crap you added to thin it....