As much as I am loathe to admit it, D's right on this one. It would take minimal additional thrust from the engines to overcome the opposing motion of the treadmill, mostly due to the effects of lost energy due to friction in the wheel bearings. When you stop to consider the fact that the wheels on the plane are essentially there to keep it from having to slide around on it's belly, the answer becomes rather obvious.
Let's put it this way:
Remove the wheels completely and allow the plane to be suspended by, I don't know, some anti grav unit that's only strong enough to lift it a few feet off the ground. The jet turbines engage and the air is compressed, fuel added and combusted,, then allowed to expand again, providing thrust (if you want I could go into the specifics of the Brayton cycle, but I doubt anyone's interested). All of this happens completely independent of any interaction with the ground. The ground could be screaming backwards at 2x the speed of sound and it wouldn't bother the jet. We're not worried about lift here, we're just talking about simple horizontal locomotion. (the lift comes as a result, but it's rather inconsequential to the heart of the problem)
Let's put the wheels back. Now the wheels, of course, are not the ideal suspension device the theoretical anti-grav unit is. There are inherrent innefficiencies, including the aformentioned friction. This would, indeed, cause some small amount of backwards force. But the magnitude of that force and the resulting motion is negligable compared to the thrust that the turbines can put out.