Nope, not unconstitutional at all. The two governors simply work out an agreement with each other. Most states have some sort of reciprocal agreement with their neighboring states already, so that in the event of natural disaster they can request NG troops from their neighbors.
Usually, the way it works is that the troops are attached to a local unit, which means that the local unit is responsible for supporting them but has no UCMJ authority over them. That's very, very typical for relatively short-term deployments.
Thanks for the infomation. It is very interesting. I think Article I Sec.10 would govern this situation because it is illegal for states to enter into any agreement without the consent of Congress unless there is an emergency that will not admit for delay. The fact that the NG is not being allowed to use guns is ridiculous, but it also implies a lack of urgency. This section does however, provide that states may enter into compacts if actually invaded. The ironic part is that by urging the states to do this Bush is implicitly admitting legally that the US is being invaded. In any case, here is Article I Sec.10:
No State shall, without the Consent of Congress, lay any duty of Tonnage, keep Troops, or Ships of War in time of Peace, enter into any Agreement or Compact with another State, or with a foreign Power, or engage in War, unless actually invaded, or in such imminent Danger as will not admit of delay.
So, based on that, isn't it absurd to send unarmed troops to the border?
I.e., can they not carry out their engineering duties while carrying a weapon? How does that work when they are doing the same thing in Iraq? Aren't there at least armed troops standing guard?
It seems unwise, to say the least, to be anywhere near our southern border without a weapon.