I do not agree with most of the points made in the first two answers. They are true, but they do not make the Vietnam War different than other wars.
The war was not the first one that was vigorously opposed by people within the country. The War of 1812 led to talk of secession in New England. The Mexican-American War was strongly opposed by Abraham Lincoln and most other Northerners who opposed the spread of slavery. The draft in the Civil War caused riots so big in New York City that troops who had just finished fighting at Gettysburg were rushed to the city to suppress them (and there were other riots as well).
Propaganda was on both sides during the Revolution, the Mexican-American War, and the Civil War.
To me, the third answer is most correct. This was the first war fought under both of two conditions:
- The war was not "necessary" in that the US had not been attacked (unlike WWII)
- More importantly, US society was much more individualistic and self-centered than it had been before.
When you combine these two (along with the TV aspect cited in the first answer) you get discontent. The mass of Americans were, by this time, much more aggressive about personal rights and privileges than they ever had been before and that is why the protest was so much more widespread than in any other war.