Toe or Tow?

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I just read an opinion column in NRO which included this: "If Larry Summers is ousted for failing to tightly tow the liberal line...."

Larry Summers aside, I have always thought the expression is "toe the line" as in line up straight along the line in the dirt, i.e. follow orders with good discipline. In this context, "tightly" makes sense: get yer toes right up tight against the line.

"Towing the line" also makes sense, it just isn't the spelling/meaning I've always assumed. Towing tightly is still ok, as it would suggest pulling rather strongly.

So, are both ok? Only one? If so, which? My lexicological universe is teetering.

UPDATE: Well, at least I'm not alone. Howard Kurtz: "Ari, and now Scott, toe the company line."
Click here: washingtonpost.com: Media Notes Extra