I'll agree with the above and say that 1000 streetable horsepower is certainly achieveable, but like I said before, cheap becomes relative and is probably directly inversely proportional to the lifespan of the engine.
Lets say for example you have an 440 with a forged crank, stock forged rods, you put some forged slugs in it and premium fasteners with some ported stock heads, just a good basic performance rebuild with nothing fancy. This is maybe a $5000-8000 build depending on how much work you can put into it yourself. Then put a big huffer or a couple of hair dryers on it for another $5000-7000, and a multi stage nitrous set up for a couple grand, and your at 1000 hp for $12,000 to 18,000. Certainly not a fortune, but is that still in the realm of cheap for you?
Then there are the aspect of streetable and longevity. So long as you don't spin the pee out it, it certainly may live for a while. IMO, rpm is harder on an engine than the boost would be, but, big amounts of boost over time will fatigue the stock parts and you had better have a regular tear down and inspect scheduled to catch problems before they become catastrophic.
Like others have mentioned, there is also all the support systems around it that will need stepped up to maintain the streetable aspect. Bigger cooling system, stronger clutch, stronger rear, stronger chassis, etc. If there are guys on here singing the blues about how their 318 4bbl has cracked the leaded seams in the a pillars, then a 1000 horses will turn a quarter panel into a taco.
1000 hp is not an impossible feat, but will require a fair amount of money, a fair amount of engineering, or decent amount of both to get there.