Note that small foreign cars DO NOT have a frame! There are very few exceptions, such as the old Honda S600 roadster and other MG Midget/MGB sized Japanese cars, but they will likely be expensive. Pickups, on the other hand, all have full frames with few exceptions. Cboy pointed out one problem -- the bulky and relativel ugly front suspension.
That said, I've often considered such myself. I'd start with the smallest pickup I could find -- an old Dodge Ram, Mazda, Chevy LUV, Ford Courier, Toyota, all early to mid 70s -- nothing as new as a Ranger or S-10. Should be able to get one for near junk prices, though the engine is liable to be junk also (who cares?). After stripping off the body (but don't destroy/dispose of it just yet!), I'd mount the engine where I wanted it and and look at that front suspension. One way to handle that would be to hide most of it. Put the radiator in front of it and see how that works. If you can live with the looks mount the cab right behind the engine. If the back of the cab clears the rear wheels perfect! Cut the top off the cab and use that for your "tub"!! Build/buy a model A/T looking bed, do a little metal work around the cowl (probably stretch/fair it out a bit), and get a radiator shell. Motorcyle style fenders for the front is fenders are required. The four cylinder front springs will be about right with the engine set back, and the pickup rear leafs should be about right too. Moving the engine so far back puts more of the load on the rear springs than the empty truck had, and less on the front springs.
If the cab is to wide it would be easier to take a chunk out of it than to build your own tub. Unless you want to build something more along the lines of a T roadster -- pretty much a flat deck with "wrap around" bucket seats! Not sure you could get that licensed though. With the truck frame and cab, you could legally license it as a whatever year truck, another reason for using a modified cab as a tub. Might have to section the cab too, or chanel it over the frame. That would be some work, but would eliminate a lot of paper work for registering the thing.
So what to do about the front suspension if it just doesn't look right? "Front half" that frame! Cut it right behind the old crossmember and make a stub frame for a straight axle. That will greatly reduce the fab work and material cost. New steel isn't that pricey, but the way. If you have to pay someone to weld it that's a different ball game!!