SSTO can't work with current technology.
More exactly, reusable SSTO.
As bizarre as its sounds, Saturn stages, taken separately, could have been SSTO.
I mean, takes a S-IVB, put in on the pad, light the J-2. The things will go to orbit; it is light enough, and as enough fuel.
Problem n°1 : you won't recover it. It has no heatshield nor landing system. If you add them, the S-IVB become too heavy, and can't go to orbit.
Problem N°2 = Payload is very weak: nearly all the stage is fuel (92%).
the SSTO problem is as simple as that.
What works (as of today) is TSTO, two stage to orbit. That give you something reusable.
Until the 90's the stages had to be winged to be recoverable (a bit like the shuttle).
Then come the Kistler K-1 team, with a genial idea : land the stages using parachutes and airbags.
That's much lighter than wings, undercarriage, cockpit, tail...
The Kistler K-1 is much less glamourous than a spaceplane, but would probably works better.
Add a reusable Apollo capsule on top, and there you are, a fully reusable manned spacecraft.