It's out by the mid-1980s at the latest. Conscripts cannot be adequately trained to handle the influx of high-tech equipment and more complex performance required out of modern Soldiers. That, and we could not have afforded to maintain a large enough Army to handle a large influx of conscripts and still equip it to 1980s standards, much less 1990s. You really, really don't want to think about the cost per rifleman or sapper on the ground today. Once it became apparent that this is the case, conscription would go.
Conscription would also fall apart when it becomes obvious we don't have anything to do with most of the population of America. 50% of US High School graduates cannot enlist in the Army because their test scores are too low. Large quantities of them are too frickin' fat. Modern war doesn't have a role for border-line retards that might have made fine line infantry in Napoleon's day. Forest Gump couldn't fill a radio with crypto.
You also have to look to the discipline problems of the 1970s Army. Yeah, those are conventionally blamed on Vietnam. They can also be blamed on a culture of disregard for conventional institutions, societal acceptance of drug use, etc. You can't polish a turd. Only a volunteer Army could have fixed those problems in the way it did (late 1970s), which was to institute programs to kick drug users, racial troublemakers, and people who just didn't want to play by the Army's rules OUT.
And Iraq? Afghanistan? With Conscripts? A nightmare. Undisciplined, untrained morons with inadequate shake and bake NCOs cannot conduct proper, effective COIN operations. You need real professionalism down to the rifle team, because that corporal or buck sergeant just might fuck up hard-core enough to get on the evening news and cause riots from Indonesia to Morocco. Not to say it hasn't happened with professionals, take the idiots from 2-17 IN up on charges now. But it would be 100 times worse if the leaders had 12 months in the damn army before taking over a team.