Michael, you might want to look at some of the threads in the Gun Law forum. The time to get your LTC varies with what town you're in, what the CLEO's attitude on armed citizens is, and sometimes, I suspect, the phase of the moon. Some people have reported getting their LTC in 2-3 weeks, and one guy in Worcester took something like 5 months or more.
This is one of the big problems with letting the local chiefs do this. Some of them are no more than petty tyrants exercising their petty little egos, and some of them believe that the Second Amendment DOES apply to individuals and act accordingly.