It has almost nothing to with that. It's hardly a matter of drilling. When I mention those with that kind of power, I am referring to OPEC along with the big oil companies. "Big Oil" has won the power struggle with the neocons to determine the future of Iraqi oil and they don't want it flooding the market (which is what the neocons wanted). It's also been theorized that part of the reason Saddam had to be taken out was because he was overproducing and exceding the the Iraqi quota set by OPEC. It's those that control the flow of oil that have the ability to manipulate prices. The big oil companies aren't going to take steps that will reduce their profit for the good of mankind.
There's also this thing called the "Strategic Petroleum Reserve". It's a stockpile of oil under goverment control to be used in the event of an emergency. In May of 2008, Congress voted unanimously to suspend stockpiling the reserves until the end of 2008. The hope is that this oil that is normally stockpiled will find it's way to market and help ease prices.
What 'big oil' companies have got contracts in Iraq so far?
I know China ,South Korea and maybe India is in ,France perhaps and the UK got a big nat gas contract but help me out with the Iraqis being big oils puppets.Even the service contracts,which in essence were peanuts,that were awarded to some of the bigger companies were rescinded by Iraq