If you want to incentivize military service then make it mandatory and many of the best candidates will enlist in exchange for some influence over their military occupation. If the worker shortage persists, and all indications are it will, this is a probable outcome.
To @downrightmike who thought the Pat Tillman tragedy was worthy of mention in such a disrespectful way, the guy's sacrifice is awe inspiring regardless & your spin on what happened is inaccurate.
But more importantly, there is no actual shortage of potential recruits. There is a shortage of recruits who meet the current military standards. You can very easily lower your standards and get more recruits from the pool that is currently disqualified for medical issues, criminal record, and general stupidity (that is, more stupid than the military currently is).
The reason why this isn't currently done is that the military doesn't need the bodies that badly, certainly not badly enough to justify the increased expense and frustration of increased shitbaggery.
The recruiting budget is huge, and I'm sure that the military is happy to mull this over in hopes of getting more high-quality candidates. If it doesn't work, they'll try something else.
The political leadership doesn't want conscription because it makes the public care a lot more about decisions to use the military.
Conscription would be political suicide. The better bet is on more automation to better leverage a thinner spread of recruits.
Sorry, not saying automation is the solution. If China bombs Guam, yes, we'll need conscription.
But conscription is far from "probable." I'm simply arguing that Congress pumping godawful quantities of money into automation is more likely than POTUS enacting a draft.