Does it violate the 13th Amendment for the Democrats to cut off pay for active duty military? *UPDATED*

Here’s J.E. Dyer about the administration’s threat to cut off pay to active duty military:

The possibility that the military will be required to continue on duty without pay also highlights one of the important differences between the military and the rest of the federal government.  The government can’t require its civilian work force to operate without pay. Its only options, with the civilian work force, are furloughing employees and shutting down services.  The civilian work force is protected by union agreements and labor laws in this regard.  The troops are not. (Emphasis mine.)

I agree that the military is different.  Ordinary labor laws could not possibly apply to them.  (“Excuse me, I have to leave the battle now.  It’s time for my union-mandated coffee break.”)  I understand too that even some Constitutional rights don’t apply to them, such as Free Speech, which can be limited because of national security.

However, can our troops really be used as slave labor, forced to work for free?  Even prisoners get wages.  Here’s the text of the 13th Amendment:

Section 1. Neither slavery nor involuntary servitude, except as a punishment for crime whereof the party shall have been duly convicted, shall exist within the United States, or any place subject to their jurisdiction.

Section 2. Congress shall have power to enforce this article by appropriate legislation.

Unlike the military (or, at least the military as threatened by Obama), I’m working for pay now, and don’t have the time to do research into the ways in which the Courts have interpreted the above language.  As I said, I know there are prisoner labor cases, and perhaps there are even cases that apply directly to the military.

Do any of you know specifics about the 13th Amendment and the military?  Do any of you have an opinion about this?

UPDATE:  My friend AJStrata is up in arms about the threat to the military, which he thinks would be a spectacularly stupid move on the Administration’s part.