Next week, meaning 10/19/13 -10/26/13, or next week meaning 3/21/13 - 3/26/13, as you asked in your message?
Can't help you with the latter, but the former, they should be.
In any case, there are tons of private campgrounds not far off the Parkway in case you get into a jam, and I imagine they've all been doing a boom business, and should be open.