According to Spaceflight 101, the fueled mass of the first stage is 403 tons, and empty mass 18 tons. Its specific impulse ranges from 282 to 311 seconds going from sea level to vacuum, implying exhaust velocity of 2766-3050 m/s. Plugging those values into the rocket equation gets you somewhere between 8600 and 9500 m/s of delta-v. I don't know the exact specific impulse curve through the atmosphere and can't be bothered with the calculus anyway, but I'd guess it's nearer the low end of the range since the rocket is spending more time moving relatively slowly in the lower, denser part of the atmosphere.
Delta-v to low earth orbit is about 9.3km/s to 10km/s depending on launch site and destination orbit, so F9R doesn't have quite enough oomph to get there.
It's pretty close, to be sure. Could it be modified to do it? The F9 has already been "stretched" once (F9 1.0 to F9 1.1) and the engines improved a couple of times, and they're hoping to increase the performance another 15% (mainly by increasing the fuel density with further cooling). If they can achieve that, then they should be just barely able to orbit the first stage, with better than 9900 m/s of delta-v -- and zero payload.
If I've got the math right, in the Falcon Heavy crossfeed situation, again with no upper stage or payload, the boosters would provide another 2800 m/s of delta-v to the stack, for a total of about 12 km/s, so it can comfortably reach LEO. As far as the rocket equation is concerned, though, that's a two-stage rocket; it just has some engines in the wrong place.
Re-entry and recovery, on the other hand, is probably impossible. The first stage is designed to withstand a much more modest aerodynamic situation than re-entry from orbital speed. Structurally and thermally, it's a completely different world.
SpaceX would like to make the second stage reusable as well as the first, which would require them to solve orbital re-entry for a rocket stage but on a much smaller scale. Even if they don't accomplish that, a fully reusable first stage would offer them a huge competitive advantage. They have no need to do SSTO.