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How would you say "Let's do that this afternoon."? I can't think of any other way to say it that isn't terribly awkward, and surely both "this afternoon" and "Tuesday" are noun-phrases.

Hmm. You're right that there's an inconsistency there, but at least it's a consistent inconsistency: "We'll do it this month" / "We'll do it in September". And in "Let's do that today", "today" is just as much a noun as "Thursday". In US English, is using a preposition for "Tuesday" or "September" optional, or actually wrong?

Peter