Brake pedal is really stiff

ESP47 said

Just an update...

Had all 4 drums turned. Bought new shoes, they all fit perfectly. Pulled all wheel cylinders out and replaced with correct Raybestos cylinders. Bought original Raybestos master cylinder. Bled MC, bled brakes and still have the exact same problem. Car is going to be taken into a shop as soon as I get some money for it. I'm fed up with this. It should not be this difficult to get a damn drum brake system to work correctly. There has got to be some kind of built up pressure somewhere because the pedal is stiff and doesn't want to be pushed down very far and the brakes are really weak. I don't even think I could lock them up if I tried. Yet when I bleed them the pedal will drop to the floor once I open the bleeder. It just makes no sense.

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These things almost always turn out to be something stupid and overlooked. Now that you've replaced virtually all the major components, here are a couple more ideas for you:
Correct pushrod or master cylinder used?
Pushrod seated correctly in recess of master cylinder?
Pushrod retainer seated in it's groove on the pushrod (manual master cylinder)?
Pinched, crimped, or bent hardline?
Pinched, crimped flexline (hose). Flexlines can also appear perfect on the outside and be broken or collapsed internally enough to block fluid flow. It might be possible for a bad hose to block under pressure and still allow fluid to flow in a no pressure situation (like bleeding).
Might not hurt to check the condition of all junction blocks and line fittings to make sure you are not getting a blockage at one of those.