With the current state of the world economy i.e. strong growth and high demand for petroleum products, I believe that if America cut it's demand for OPEC oil, currently at 16% of our use, OPEC would be able to raise prices to make up for part of the revenue shortfall. India, China and the other heavy users would pay the price simply because they need the product. It would be a balancing act for OPEC to keep the prices low enough to sustain the worlds economic growth yet high enough to make up for the income loss from America not purchasing from OPEC any longer. If they push it to high the worlds economies slide into recession and nobody will need their oil, at least not much of it. I realize this flies in the face of the market mechanics of supply/demand but it just may work.
If America stopped buying Arab oil, the only way they will be able to raise prices would be to drastically cut production, not only by the 16% we would no longer be using but also enough to cause a shortage so they could raise the price.
Put another way, if they raise the price, people buy less. It might work in the short term, but everyone knows that the Middle East is not the only place where there is oil. If the price goes up enough, there are a lot of oil fields elsewhere that will suddenly become economically viable.
So the Arabs might be able to raise the price, but they could end up with less revenue.