Because many hotels may have guests who decide to stay for additonal days after checking-in (as well as having no-shows) your room assignment may not be made until the morning you check-in, or possibly when you are actually completing the check-in process.

Is a chance of getting this room worth $10 to you? Can it possibly cost more than that to make the call to get a request put in? If you still don't want to make the call, try googling the actual hotel (search for the GM's name if possible) and send an email. If you send an email to "customerservice@ followed by whatever hotel you're staying you will be less likely to get what you want. If you're staying at something like a Four Seasons, Ritz, Manderin etc perhaps you could try calling a more local location as "service" is supposed to be high on their lists and they may be willing/able to assist you.