If we brought back the draft in such a way that everyone had to serve the country in some capacity, it is very likely that very few people would be happy about it.
The military certainly does not want to have a draft. They feel that the experience of the Vietnam Era shows that a draft is not a good idea in the modern day United States. They want to have a military made up of people who really want to be there, not a large group of reluctant draftees. In addition, there is simply no need for a military of the size that ours would be if everyone were drafted.
This would likely mean that we would have to institute some sort of other national service requirement. This, too, would probably be very unpopular. Large numbers of people who were required to serve in it would be very unhappy at having to put their lives on hold to serve. Many people would feel that such forced service is un-American. Other people would be very unhappy about the cost of administering such a program. They would feel that it was a real waste of government money for no good purpose.
There might be some good effects. People might feel more connected to their country. But the good effects would not be sufficient to overcome the negative attitudes that most Americans would have about the program.