So you are looking used. Nothing wrong with the offer you suggested. Used cars have better margins than new.
Any private sellers within a couple hours of you? They love cash deals. Check Autotrader if you haven't already - might also check Craigslists for cities in a 100 mile or so radius.
That's what's driven me to the lots. Normally I'd avoid the lots if at all possible, given my past experience.
I'm in Knoxville. Anything in good shape, with reasonable miles at a reasonable price, that hits CL or autotrader is gone within what seems like hours. I'm up to 7 different cars I've called about locally that were already sold (or had a deal pending that ended up going through). Meanwhile, the ads show the same 15-20 mega mileage or hilariously overpriced or salvage titled vehicles that have been on there for weeks.
I check the Asheville, Birmingham, Chattanooga, and occasionally Atlanta and Nashville craigslists. I've found some deals, but nothing survived until the weekend when I could get there to look at it.
I realize a lot of this is because I'm shopping mostly Subarus, which I'm learning attracts a different type of customer (dedicated to the brand, willing to pay a premium even on used, etc. Which now that I say that, lends more creedence to Nerd's point about demand). I may be generalizing too much, but that seems to be the case.
Its definitely a lesson in patience.
On the bright side, its a hell of a time to be selling decent, "cheap", used cars. My wife's 04 Accord has at least 3 people wanting it once we find her something else.