Domestic Oil Production: a potential remedy to rising oil prices?

I found this piece on America's oil particularly interesting because of Nat's presentation last night. One question I had was how much of an influence does OPEC really have on oil prices? Also, according to the EIA, only 51% of America's oil is imported, and of that 51%, almost half (23.3%) comes from Canada and another 10.3% comes from Mexico. Since 1992 we've imported more oil from non-OPEC countries than OPEC ones. So how much could increasing our domestic supply of oil really "send a message" to OPEC anyway?