It depends where you are from. I am from Cali so If you have a rock-solid car here and drive primarily within 10 miles of home/your mechanic, then waiting till the same day is fine. I recently had to find a way to get a car 25 miles away and looked into AAA to do the job. It turns out, at least in california, you can only sign up for the regular membership which is $40/year, which only allows for up to 7mile tow. You have to wait 90 days to sign up for the premier service which will allow the 100mile tow. I asked the guy if it was so people didn't abuse the 100 mile towing service like I am and he laughed and nodded his head.
In the end $100/year is not very much for peace of mind knowing i can get my car, or any of my friends cars that I am a passenger in towed for 100 miles for free. I can certainly find the $8/month to cut out of my eating out budget, or going out budget, or gas budget, etc. every month.
Just my californian 2 cents.