Hi Robert,

It depends on context, but either can be a correct expression.

Toe the line means, as John pointed out, to conform. It comes from the military wherein troops are required to stand in ranks, or to stand with their toes touching the same imaginary line as their neighbors.

Tow the line means something very different. It means to do your share of the work. It comes from the old days of barges being moved through canals and streams by people or pack animals trudging the bank while pulling (towing) a rope (line) tied to the barge.

The two expressions become confused when they are both applied to party politics. If you're a grass-roots worker trying to convince others that your party is the better choice, then extolling the virtues of the party platform is your fair share of the work. And in order to be effective in your task it is necessary to make certain that you are singing from the same page (so to speak) as everyone else in your party, or arguing for the same party platform. Thus, it really can be the case that "towing the party line" (doing your fair share of the work) is "toeing the party line" (conforming to the party platform).