He did. It was the "daisy ad". I remember it very well. A little girl was picking daisy's in the foreground and humming an innocent tune and then the nuclear bomb went off in the background. It was monumentally effective. Goldwater was portrayed as ready to nuc North Vietnam and people believed it. Heck, he had already threated to bomb them back to the Stone Age if they didn't back off. I doubt North Vietnam would have carried on a war against us if Goldwater was President. He didn't take any crap off Communists. He knew them for the evil they were.
Truly, it was a monumentally effective political ad. Everybody from that era remembers it well.
What you may not know, however, is that the Johnson campaign paid to air "Daisy" only once -- during a September 7, 1964, telecast of David and Bathsheba on The NBC Monday Movie.
Johnson's campaign was widely criticized for using the prospect of nuclear war, as well as for the implication that Goldwater would start one, to frighten voters. The ad was immediately pulled.
However...the news media continued to use the ad in their analysis of the presidential campaign -- often airing it in its entirety. Altogether, "Daisy" was aired on network media over one hundred times. But the campaign paid for its airing only once...
The military industrial complex profit gaggle who owned Lyndon wanted a drawn out war to increase profit margins and manipulate currencies. Goldwater might not have been in their pockets, so lies and full media whoredom blitz was used to portray the man as insane. Evil is enhanced when devils like LBJ are in power. Kind of like now, with little barry bastard boy of the current regime peddling racist as his schtick, his zeitspittle.