“such a deployment would beg to be federally activated. DOD has a much bigger pot of money.”
I think that this might be how this issue came up - Federal budget preparations, to potentially reimburse States. The budget is starting to shape up, and everyone is getting their placeholders in for the upcoming winnowing of priorities.
My understanding is that new funding for starting wall construction is expected in April (maybe May). It is possible that some Guard units might assist (SeaBees, or Engineers), stand guard (Infantry), or respond to riots/demonstrations (Military Police). Even if it is not part of the plan, it is a reasonable contingency preparation.
Now hearing Trump might have considred this idea only as a ploy to catch leakers. Multiple copies each with slight variations were handed out to multiple parties. Depending on variation leaked, they’d know who leaked it.