IT people routinely have to deal with the need to be on-call. Sounds like you are part of a relatively small shop and the boss (with all due respect) likely is more trying to make sure he can get stuff done as opposed to flattering you in any way. If when you were hired there was no mention of being ‘on-call’ then the job description has changed and you should feel free to point this out and request additional compensation. Most companies have it as part of the job description and thus build in the extra hours and incovenience into the salary or specifically put a bonus structure in place to compensate the workers.
On a personnal level, if your wife is objecting there is a problem. Don’t put the job or your duty to work before your duty to your family. Set limits with your boss. Try something like the phone will be on your person between 6am and 7pm. This means you can be reached before most people get to work and for a time after they leave. Any other time, indicate that the phone is likely to go to voice mail and you will make an attempt to check it when possible. There are other jobs out there – but you only have one family.