G'day rnordquest,
I dunno about the B737 but on the B767 & B747 there is both a tiller and also nosewheel steering through the rudder padals. The rudder pedal steering has limited authority, about 7deg either side of centre, while the tiller gives full control and overrides the rudder pedal steering.
Directional control during the takeoff run initially is through the rudder pedal steering until the rudder itself becomes effective, at around 40kts, then the nosewheel castors. It's all mechanical and it all works well.
In the event of a nosewheel steering failure the aircraft can still be steered by using differential braking and or asymmetric thrust.
Regards,
BH.