Illegal Immigrants and the War in Iraq: Can one solution solve both problems?

How to solve both of these problems with one solution is challenging at best but not so remote as one would think. Try this on for size.

The problem we face in Iraq is that our military is broken and we aren't able to recruit enough new soldiers to relieve those in Iraq on any meaningful and predictable schedule. Many soldiers are on their 4th tour of duty with little time at home with their families. I have proposed that we institute a DRAFT in recent postings, which has not been popular with our elected officials because they know there would be a backlash with voters back home in their Districts.

But here's a thought. If there were a DRAFT and it required every person 18-25 years old to register again, as was the case when we had the DRAFT before, with a Selective Service Dept., any persons of this age group without a Selective Service card would automatically be Drafted and required to serve at least 2 years. All illegal immigrants would fall under this rule by just being here, and while we wouldn't return them back home, we could bring them into the military and have them replace current troops serving.