The tires are just rolling. They are just there. Heck, they don't have to turn at all given enough wind to have the plane take flight. It doesn't matter what they are doing.

Until the friction being created by them rolling overcomes the thrust provided by the jet engines the plane will be able to get enough speed to take off.

You're caught up on the wheels and for some reason you keep thinking they are propelling the plane.

Lets say your on rollerskates standing on a moving sidewalk. For arguements sake lets say your stationary to the rest of us and the walkway is moving underneath you without you having to do anything to brace yourself to stay in place.

I walk up behind you and push you forward. Do you move? Lets say I pass you a tow rope and walk along side the moving walkway and pull you against the traving sidewalk direction. Do you move in the direction I pull or do you stay still?
Would you still move if in my direction if the sidewalk was going 2x faster than I was walking?

Just think of the jet engines as a tow rope.