You already know it won't be 10 hours-- maybe6-7-- given the time to get through Immigration and Customs and then come back for your onward, domestic flight. Under that if you need to allow time to rent a car and return it. The amount of time you'd actually have in DC, after finding parking, could end up being fairly limited. If it's a weekend, traffic will be less than on a weekday, obviously, but I still think it would be a bit of a rush. If it's your only chance to see DC at all, even a quick drive-by (so to speak) might be worth it.

How early you can check your bags for your onward flight (i.e., whether you can just hand over your checked bags at the transit desk outside Customs) can sometimes vary by airline, so first thing is to call them first. We're assuming you're on one through ticket, and that the two airlines have an interline agreement for the transfer of bags (e.g., not transferring to Southwest). I haven't seen the Air & Space annex near Dulles but would like to. I'd probably shoot for that in your situation. But it's your trip.