I don't know how old you are but putting the blame for US public's anti-war sentiment on the media is only barely accurate. Any 18 yo HS senior in 1967-1972 knew kids just a year or two older who were maimed or killed before reaching twenty. Their mothers all knew mothers who lost sons in VN. And both groups knew that even a little money or influence kept you safe. The poor and the working class (America was a country full of Blue Collar workers then) were paying the price in a big way while the middle and wealthy classes were able to avoid most of the loss. The truth about America during that war is that if you were unlucky enough to have a brother/son/yourself sent to fight or eligible to be drafted then the war consumed your family. If you did not, then the war barely made it to your screen. A mother burying her 19 year old son and looking at two more coming up didn't need Peter Jennings to tell her something was seriously wrong.
If the draft had been fairer and the burden spread around more, do you think that it would have changed how you and your neighbors thought about the war?
If the war had been fought by a larger army of enlistees and volunteer reservists, without recourse to the draft, do you think it would have been seen differently by your neighbors?
At any one time, U.S. Army troops in theater never topped about 520,000, plus less than 100,000 Navy and Air Force -- basically the same size force President Bush was able to put together for the Gulf War, with a volunteer military and a reservist and National Guard rear echelon. He amplified the U.S. effort with allied contributions adding up to about 200,000 men, but the U.S. level of effort was about the same as that for Vietnam, and it lasted about six months to a year. The U.S. was engaged at or near those levels for about two years in Vietnam, and another four years, maybe, with troop levels about half that.
The current limits on the size of the military are mostly budgetary and limited only by the willingness of the Crusterati to pay the taxes to pay for it. It's a lot smaller than it was during the Gulf War.