I, the spaceship, would like to accelerate through space. I take up some fuel and hurl it in the opposite direction, which requires me to apply force to the fuel I'm ejecting. It goes off into space at some rate determined by the impulse I applied and the mass of fuel I applied it to.

Newton's third law means that when I hurl the fuel, it applies a symmetrical impulse to me, accelerating me in the opposite direction.

In this model, the acceleration I get from the fuel doesn't depend in any way on the mass of the fuel I eject, only on the force I apply to it. What's wrong with the model?