It depends on the MOS you have chosen to enter. Combat MOSes go through OSUT (one station unit training), and since each training cycle has only a limited number of openings, and start only at certain times, it's possible for classes to fill up, forcing you to delay your entry until there's an opeining in a later class.
For example, when I went in, the time I had to wait for the earliest openings:
MOS 11B w/ airborne option: 12 weeks
MOS 19K: 8 months (the M1 was new then, and everybody and his fucking brother wanted to be a tanker)
MOS 19D: 3 weeks
MOS 13B (which is what I chose): This was on a friday, and I was a gone MFer on Monday [:D]
Keep in mind, though, that Army recruiters DO have a quota, and he WILL BS you, just to get you in. He has ZERO ability to promise anything. The guy you will talk to at MEPS, the career counselor, is who you get the REAL deal from, and it's HE who schedules everything, and it's HE who writes up the contract.