The US Army and Marine Corps are massive users of supplies hauled a long distance from secure rear area bases, up the roads to large consolidated logistics bases, and then spoked and hubbed out to the forward operating base camps. Here the last few gallons of the barrel that started in Kuwait are poured into the tank or MRAP or the base generator that powers the radios. Fuel and easy access to fuel is ultimately one of the American military's great force multipliers and core competencies.
Noah Schactman over at Wired's Danger Room has a good (but slightly old) graph of where one particular type of fuel for daily operations in Iraq comes from. Notice how there are only three entry points, and one, with approximately 15% of the total load is coming in from Turkey and travels through Kurdistan before reaching major US bases. As Cernig noted yesterday, there are 140,000 Turkish troops ready to invade northern Kurdistan, so I have severe doubts about the willingness of Turkish civilian truck drivers to drive through Kurdistan if the Turkish Army crosses the border in sustainable force.
Another 15% or so of the fuel comes in through the Anbar desert which right now is slightly safer than it has been over the past couple of years, but it is still one of the leading areas of insurgent activity. The last major route with 70% of the throughput is the Kuwait City to Baghdad route. USA Today notes that convoy busting is becoming a popular activity among insurgents, militias, and criminal gangs in the south.
Just keep this in mind --- if the fuel supply lines are cut, the US Army and Marines are immobile and operationally useless....