Let's say that the minimum wage for civilians is raised to $15 an hour. If a high school graduate can land a full time job at $15 an hour they're going to make $31,200 a year.
If Billy can make $31k a year flipping burgers why would he risk his life volunteering for the military at $20k a year? So, just to remain competitive, the military will have to raise base pay (and the entire pay chart to be equitable) by $11k (a ~55% pay increase). Not the $131 that they should by all rights be earning, but still there's no way the budget can support that big of an increase.
So, if Billy and all his friends aren't volunteering for the military because they're making more flipping burgers or working at the car wash (great movie and song, btw) then what does that mean?
It means a return to the draft (aka selective service). Let that sink in. The government can pay a draftee whatever the government feels is appropriate. The SJWs have actually made the return to the draft easier by advocating for women serving in combat and gays and trans serving openly. I say bring it on. No deferments for anyone. Are you in college? Too bad, finish either by taking classes while on active duty or pick up your studies when your enlistment is done. Married and/or have kids? Too bad, but Uncle Sam will help take care of them. Plenty of volunteer service members have dependents, the system is in place. Got bone spurs or asthma? No problem, plenty of desk jobs and drone pilot jobs out there that you can fill. Don't want to or absolutely can't serve? Fine, do an equivalent hitch in AmericaCorps or some similar outfit.
Sorry that this is so long. The moral of the story is BE CAREFUL WHAT YOU WISH FOR!