hotel - any that will take "day" reservation or a very, very early check-in?
 

arrive on redeye at 6:30 - leaving in the afternoon. DC

And that would be where?

wait a second I guess Washington DC?

Yes, Washington DC (Dulles)

You might be better off reserving a room for the night before with guaranteed late arrival (call the hotel front desk and explain how late), with a late check-out option. Or, priceline it for two nights if you can get it cheap enough if late check-out won't work.

for "day rates" you'll have to contact a hotel directly.

If you join Choice Hotels' "Choice Privileges" (or "Guest Privileges") program, the hotels are supposed to do their best to accomodate a 2pm checkout. You would need a reservation for the day before AND should still note your VERY late arrival, as the policy is that they will hold your room until 7am, then cancel remaining nights.

I work for a hotel and I know that as long as we have rooms available we will rent at 10am instead of our usual 3pm check in time.

oh I forgot to say. If you have a reservation for the day you would need an early check in your chances of getting a room early in the day are better. I would call the hotel and confirm everything though because every hotel is ran differently.