Step one: make sure people are desperate in order to make them forget who made them desperate once the check arrives.
For too many people, it'll work.

The reason I ask is that it's a perfect Trumpian double move to 1) "give" a bonus that's actually coming from money many military members would already receive and 2) create a bigger tax liability for them by doing so.

More like your parents taxing your allowance to buy you a Christmas present.

Military personnel will have to pay taxes on money that was supposed to supplement their housing.