_Tow the line_ may well be one of the reshapings that will soon be considered acceptable in standard English. It is so common that it is easier to find salient examples in journalistic writing than on the general-purpose web.
Michael Quinion at Word Wide Words explains the original form, _toe the line_:
> Toe the line is the survivor of a set of phrases that were common in the nineteenth century; others were toe the mark, toe the scratch, toe the crack, or toe the trig. In every case, the image was that of men lining up with the tips of their toes touching some line. They might be on parade, or preparing to undertake some task, or in readiness for a race or fight.
The “lining up for a race or fight” metaphor has been obscured, and a new, nautical imagery has been grafted on the expression, thus changing the spelling. In particular when a blend with compounds like _party line_ occurs, the original metaphor slips farther into the background: a party line is not the kind of line that can be toed. And then it is but a step towards towing the line in a particular direction.
An example for the ideas that underpin the semantic reshaping that has taken place is provided in this commentary, on a blog, by a person named Rog:
> Okay, hang on. I’m pretty certain that “toe/tow the line” has a dual etymology, both with a nautical background. Like many such phrases, the meaning has changed over time, giving it multiple connotations.
>
> I don’t doubt that the original was likely “toe”, since that form of punishment (making a sailor stand on deck for long periods of time) is near ancient though undoubtably still in use today.
>
> “Tow the line”, however, is closer to the meaning which people usually are aiming for: to tow in a rope, usually while docking smaller vessels. It implies taking up an open task, doing your share, etc.. as opposed to punishment for a lack of duty.
A very convincing argument, but pure invention, without any foundation in the history of English.
(See also tow » toe.)