What Big_John and commando1 said. Tires stop the car. If all 4 tires skid at the same point, the brakes can't do any better than that, and functioning drums can skid the tires, and do it evenly. Of course, you want to brake until just before you skid, which nobody can judge so you skid-off-skid, i.e. pump the brakes in a panic stop, which is what anti-lock brakes do. Does anybody here really believe that drum brakes can't skid the tires? Even my Newport's massive 11"x3" front drums? Don't compare old specs for our cars that were measured with narrow bias-ply tires. The feds mandated front disks in 1973 because unskilled drivers would ride the brakes down long hills, experience fade, and run off the cliff. Disks cool off quicker. In the North Carolina mountains they can spot Florida drivers from miles away by the smell of burning brakes. Rear disks are mostly for marketing in today's cars.
Going back to the original question. Perhaps your master cylinder piston is bottoming out. If everything is factory, it shouldn't do that until the pedal is almost on the floor, but who knows what rebuilt parts have been swapped. You would have to take it off and push it in with a socket extension and measure, then compare to your pedal. Not simple. It is possible that you lost your booster. My 65 Newport became very hard to stop and I found the booster had a torn diaphragm, and a rear seal was leaking oil. If you press the pedal real hard with both feet, I would think that either the fronts or rears would skid. That should be true even if you lost one of the 2 systems in your car. In that case the imbalance warning light should light, but the switch is often rusted in place or the bulb could be out. People have also found rubber hoses failed internally and the rubber closing off as pressure builds. Bleed all the wheels until you get clear fluid. You need to do that every few years unless using DOT 5 like I do. I once couldn't get anything to flow from an 82 Aries caliper until the assistant used 2 feet and a bunch of rust gunk blew out. No more glycol fluid for me since then, even living now in bone-dry CA.
