How many flight training hours can a student realistically do in a week?
There are a few external factors 


Your CFI:
If we are talking about dual time (or supervised solos) here your CFI will need to be free. 
The plane:
Keep in mind that school may have other students who may also book the plane, or it may be out for its 100 hour inspection or it is broken etc. 
The weather:
Depending on where you are located, you may be limited by the weather grounding you for VFR flight.
The Wind:
A lot of flight schools (at least the one I go to) impose student maximum limits when it comes to crosswinds. At single runway airports this could cause an issue. You can mitigate this by training at a place with two runways.  


Now if we look past all those and assume you have a working plane, a CFI, and clear weather, then I would think (assuming the school is open) you could log 3 hours in the morning and 3 in the afternoon if you really pushed it. If you started your day with 1 hour of ground from 8-9 then flew from 9-noon. Lunch. Then another hour of ground from 1-2 and flying from 2-5 that is putting you at close to 6 hours a day. Throw a few night flights in there, some more ground lessons at night and you may be able to squeeze the time in. Keep in mind you will also need to study for the written exam.

Note: The above projection is strictly based on everything working all the time which in aviation is often not the case. Your results may vary.