There are several differences, in my eyes, between the public reaction of Vietnam then and Iraq now.  

The biggest difference is that we still have an all volunteer military. The draft really brought home to young men and their families that they could be fighting and dying in the jungles of Vietnam, whether they agreed with the war or not.  

It was also the '60's, which I think is a unique time in our history.  It was a revolutionary time and not just about sex.  It was a time of questioning the establishment and the staid morals of the '50's.  It was about standing up for yourself, whether you were young or female or black, etc.  The whole era was about breaking out of the subdivisions our society had assigned to people in general.  We also didn't have as many distractions then.  We didn't have 500 channels on tv.  We didn't have the internet, which has become a place to protest and rally people to work against the war in other ways.  In the '60's people actually had to meet face to face in someone's home to organize.  Today, you can put a notice on a blog and have people work from home sending out info via email.

There was also the difference in reporting between then and now.  We had nightly reports from the war arena on our tvs.  The reporters were showing grizzly scenes from in theater.  Sitting in your living room watching it, the violence was palpable and scary. We also saw the flag draped coffins coming home and funerals that were held.  We don't see that kind of reporting these days.  

Also, the Vietnam war raged on for over 10 years.  Here's a good history of the progression of protesting the war in Vietnam.

I do believe that, if a draft were reinstated, there would be a huge outcry and lots of people marching.  I also believe that, if this war continues on for another 2 years the protest movement will grow.