While interpersonal relationships were important, Roosevelt's mediation wasn't entirely selfless; Germany was an important trading partner both for the US and, before the outbreak of the war, for the UK, and both of them had an interest to keep it that way.
Anyway, back on topic; Austria-less Germany is somewhat hard to imagine. The Prussians simply didn't have the inclination, and of the other "Germanies" even the larger ones such as Bavaria or Hannover lacked the military or diplomatic power and - something that's often overlooked, nowadays - the prestige to pull off a true unification. Without outside backing I think the most we would've seen is a somewhat loose confederation not unlike our modern European Community, but limited to the minor German countries.
With outside backing, though, the main question would be; by who?
Someone suggested the French, but they would have no interested in a united and strong Germany; at best, they'd have either wanted to set up a puppet state in the Rhineland as a buffer or to take those lands for themselves.
Perhaps the British, after the Napoleonic Wars, decide to sponsor the revolutionaries in '48 in hopes of creating a strong counterbalance against the French? It would require a somewhat earlier PoD, though, perhaps in regards to Hannover (which was in Personal Union with Britain for a while, iirc).
- Kelenas