Dropping the external boosters and also the entire 75-100 ton orbiter from the picture, would the tank all by itself have made orbit? This would require bolting at least 5, better 6, perhaps even 9 SSMEs to the bottom of the tank. I am assuming 7 below for parity with the Shuttle's ~half-G initial acceleration.
I am grossly simplifying here obviously: 26 tons empty tank plus 7 x 3.5 tons of engines is 50.5 tons together against 735 tons of fuel mass. Sea level exhaust velocity is 3.6 km/s, and vacuum 4.4, so I'll assume 4 (optimistically, pessimistically?) to plug into the Wolfram Alpha calculator linked from the Wikipedia page on the Tsiolkovsky rocket equation which says that the delta-v to reach orbit including gravity and air drag is 9.7 km/s.
What I come out with is that I have at least 20 tons left to play with for things like a harness around to the bottom of the tank to attach the engines to, control gear and payload. Which would apparently leave at least 10 tons of payload allowance?
What the equations I used completely ignore is initial thrust to gross launch mass which'd surely affect gravity and air drag? With 6 SSMEs at ~21 tons and ~1116 tons aggregate sea level thrust I'd have a little less than the Shuttle's initial acceleration, about 1.38, with 9 at ~32 tons it would be about twice the Shuttle's. What is the assumption behind the 9.7 km/s delta-v on the Wikipedia page as to air/gravity drag fraction and initial launch acceleration?
How far off am I with this sloppy math?
EDIT: Can someone derive the optimum number of SSMEs that yields the largest payload, and share their logic? It's gravity drag vs dry-mass fraction vs air drag: More engines means less gravity drag, but worse mass fraction and also air drag since you'd get faster early on in the lower dense atmosphere, and vice versa.