Mark,
I started out with just a few properties and worked full-time. Eventually I began acquiring more - to the point that I decided to start a rental property management company (still while I was working full-time), mainly to help with my own properties.
At the start I think you will find it is usually fairly manageable with under, say, 10 units. Make sure you have a good plumber (and probably an electrician) on speed dial. In my experience most issues that need immediate attention are water / plumbing related and to a lesser extent electrical. Most other issues (roommate issues, non-payment of rent, etc) would not require you to do anything immediately while at work.
If and when you start to get to 40+ units it may be worthwhile to have a part-time person helping out during the day. 100+ units will probably require a full-time employee.
This all, of course, depends on the type of rental units, age, deferred maintenance, etc.
I hope this helps!