Agree - this one should have been an early mention. Barry McGuire sang Eve of Destruction. This video has the cover of the album only during the song. Lyrics picked up and adapted from Whitegum.com to what McGuire actually sang (he has a lot of contractions in his version and use of "Ah" and "No" in there.)

From YouTube notes: ""Eve of Destruction" is a protest song written by P. F. Sloan. Barry McGuire recorded the track in July 1965. It was released by Dunhill Records and was an instant hit reaching #1 on the Billboard Hot 100 in September of that year."

The eastern world, it is explodin'
Violence flarin', bullets loadin'
You're old enough to kill but not for votin'
You don't believe in war, but what's that gun you're totin'
And even the Jordan river has bodies floatin'
But you tell me over and over and over again, my friend
Ah, You don't believe we're on the eve of destruction

Don't you understand, what I'm tryin' to say
And can't you feel the fears I'm feelin' today
If the button is pushed, there's no runnin' away
There'll be no one to save with the world in a grave
Take a look around you, boy, it's bound to scare you, boy
And you tell me over and over and over again, my friend
Ah, You don't believe we're on the eve of destruction

Yeah, my blood's so mad, feels like coagulatin'
I'm sitting here, just contemplatin'
I can't twist the truth, it knows no regulation
Handful of Senators don't pass legislation
And marches alone can't bring integration
When human respect is disintegratin'
This whole crazy world is just too frustratin'
And you tell me over and over and over again, my friend
Ah, You don't believe we're on the eve of destruction

Think of all the hate there is in Red China
Then take a look around to Selma, Alabama
Ah, you may leave here, for four days in space
But when your return, it's the same old place
The poundin' of the drums, the pride and disgrace
You can bury your dead, but don't leave a trace
Hate your next door neighbor, but don't forget to say grace
And you tell me over and over and over and over again, my friend
You don't believe we're on the eve of destruction
No, no, you don't believe we're on the eve of destruction

There are lots of versions of this with archival footage. The next link has a hodge-podge of clips from various war periods and locations, not just Vietnam.

There are many results with curated video montages on YouTube.

A historical note: The reference to "four days in space" may refer to the August 21-29, 1965 Gemini orbits of the Earth. A Russian woman spent four days in 1963 on Vostoc 6, but is less likely to be the motivation for the lyric, and four may sound better than seven as far as the line scansion.