Looks like a lump of freakin' clay.
I guess that seems right. So now that we've determined that it actually isn't a car (come on, name me a clay car. I dare ya. No, Chevettes don't count.) the question becomes "If it were made out of painted stuff, what would it be. Besides ugly as filth." The answer is, of course, ugly as grime. But beyond that, I would imagine that it would be fiberglass, as it obviously was limited in production and a splash could be taken directly from the clay. Furthermore, it probably would be powered by somebody else's engine, because this ain't the big leagues (Just look at those grunts! If it was GM they'd be smoking Chesterfields and swilling martinis, which would go a long way towards explaining the styling.)
Stay with me here, cause I swear I'm gonna solve this.
Looking at the styling cues, I'd place this mutt in the early fifties, 'cause they didn't know much better then. It's the work of a maverick, possibly an engineer or designer, probably whose work is well known outside of the automotive arena. Thank God. Let's face it, whoever designed this probably could create a nice shoe polisher or floor sweeper but I seriously doubt if he could design even a decent Oscar Meyer Weinermobile.
Now that I've made these ridiculously baseless conjectures, I'll toss in another one: has Karn recently posted anything that meets these criteria?
Well hey, looky here:
http://www.autopuzzles.com/forum/index.php?topic=530.0 The Studebaker Sceptre by iconoclast Brooks Stevens! Why don't we check into his other work, shall we? Nuthin' over there... not in this pile neither... under this box of stuff? Nope.. nothin...hold the phone? My, my, my, what do we have here?
Of course, it's all obvious now! How could I have been so stupid? It was the cover car of the April 1957 Road and Track! The Paxton Pheonix Powered by Porsche!
So there ya have it: a little lesson in deductive reasoning, unflinching logic and a tiny dose of digging. Nothing to it.
Naturally, the bigger lesson is that such little lessons are much easier to create when you're working backwards, having blindly stumbled over the answer through sheer dumb luck.
Oops. Did I type that out loud? Dang.