Working a job while joining the militar?

NO-don't be foolish. These days its a long process from the time you talk to a recruiter till you actually enlist and then go off to Basic. Sometimes it can be as long as a year. Giving your notice like you are proposing will leave you with no job in a few weeks and probably waiting weeks or months to enlist and go to Basic. It will also give you less flexibility probably in what job you choose and enlist for so you will be basically screwing yourself in more ways than one. Call the recruiter and make an appointment and explain your situation. Most will work with you on this if you make them aware and you have some of Fridays off based on what you have said here.

You'll be in Delayed entry for at least three months , and probably more depending when a seat opens for your job.

Go when you have time, or see if you can make an appointment with them. If they're all in the same building- see if you can see all of them about 45 min apart... (an hour would probably be better)

EDIT-

9finger has a good idea too.

This is not a good idea.

There are many things, medical, legal, and otherwise, which could disqualify you from serving.

Or, you might change your mind after talking to a recruiter.

You wouldn't quit your job just to go on an interview, would you?

Do NOT quit just because you want to join. You have no idea if you will even be able to do it.

Have called the local recruiters to see their hours? Meaning Friday is possible and maybe even Saturday. Or you ask to leave early one day and go see them.

Call in sick one day and visit a recruiter. But this is not a one day process. You're going to need a few days off until you ship. Which could take up to a year.

realize, it will be from 4 to 6 months before you leave for basic