That core rocket might be able to do SSTO already. As you pointed out, the old Atlas E & F boosters from the late 1950s/early 1960s were essentially 1 1/2 stages to orbit. They were able to put payloads as heavy as a Mercury capsule into orbit. The new Atlas V uses a more efficient engine, the Russian designed RD-180, and already has a very lightweight structure. According to this source, the basic 401 model can put over 12,000 pounds into LEO. Like I said, it'd be interesting if someone with the appropriate software could run the numbers. If it come up a bit short, I see no problem with cheating a bit with solid fuel strap-ons. I'm not a purist about such things.

Whether such a vehicle would be economically viable is another matter. Suppose you could make an Atlas V without the upper stage that could put a small payload into LEO. Would that cost less per pound than other launch vehicles? I don't know.

It may be that in the near term, SSTO and reusability will be mutually exclusive. The added weight of heat shielding and landing systems might cut any payload margin so drastically that it just isn't worth doing (or may not even be possible with existing technology). There might be a way to eventually return the most expensive components, such as the engine and guidance system, but that would still require a fair amount of weight for the shielding and recovery system. It'd be quite a bit less than for the entire vehicle. Compared to the engine and guidance system, building another Atlas tank assembly is relatively inexpensive.