they are butting heads over whose plan would be better for the deficit.
to butt: If a person or animal butts you, they hit you with the top of their head. To strike or push (something) with the head or horns. To strike or push with the head or horns; ram with the head || to strike or bump against
to butt heads with: chocar con, tener un encontronazo con, tener roces o riñas con