No, no, no.
As someone who volunteered, I don't want to serve with people who don't want to be there. There are plenty of bad attitudes in the military from people who freely signed their name on the dotted line. Imagine dealing with the "Screw you Sergeant! I didn't ask to be here!" The only way to deal with these malcontents would be corporally and that would be A.) detrimental to morale and unit cohesion and B.) horribly controversial, generating enormous bad press about the military.
There are much better ways to increase enlistment and retention (pay raise, hint, hint!) than drafting people who don't want to be there and will do everything they can to get kicked out.
That being said, there are untold numbers of draftees who served in the US military with courage and honor.
Did you type "pay raise"?
The military gets one every year, and twice every other year...
Maybe someday a Reagan-type 20%+ ('81-82?) one will come around again...