My tenant texted me last night at 8:39pm that the toilet is backed up.  I called the plumber this morning and he said that he would try to make it there today but has a busy schedule.  He is a guy that I normally use and has fair pricing.  How long would you say is reasonable for a tenant to wait for a plumber.  It is the second floor apartment of a duplex and the downstairs tenant is not having an issue.  Chances are it is something they put in the toilet themselves.

This really depends on the plumber's schedule.  I know that when I need to send one of our guys out, I check my calendar first to see what I have available, then provide the customer with a time frame.  

With that being said, I would say a 6 hour window (Ex: AM or PM Appointment) would be a reasonable wait.  (Heck, I have had package/material delivery time frames longer than that!)

Again this really depends on HIS schedule & if it were me, I would have provided YOU with a time frame to avoid this confusion.  Communication is key! 

Fair pricing and quality work usually means a big backlog of customers wanting their services.

A toilet clog is likely a small fee compared to bigger jobs where more money can be made. They probably try to fit in the small stuff in between larger and likely more profitable jobs. 

Instead of an open-ended statement like, "I'll try to get there today..." you should find a plumber that says, "I can be there between 2 - 4pm."

Has the tenant actually tried plunging it? Whenever I get that call, I explain that a toilet clog is a tenant caused issue and they could be responsible for the bill. You'll be surprised how fast that clog goes away. 

And this is precisely why in my lease it states 'toilet and drain clogs are the responsibility of the tenant'. 

Once I began this practice I literally never had a tenant contact me since about a clogged toilet or drain (when they know they'll be paying for a plumber they are much more careful).

For this I would call a drain clog specialist (they are the ones with the $99 specials) - they tend to go out to a property within two hours; the one time I used one he was there in roughly an hour (it was a nasty clog too - I had some pipes jetted by a different company soon after buying a property and instead of clearing those pipes they simply clogged the main sewage pipe causing the plumbing to back up).