In 1964 I was in high school, living near Monterey, California.
I attended primary rallies for both Arizona Sen. Barry Goldwater and New York Governor Nelson Rockefeller.
Goldwater's rally was much larger, and he won the primary, though lost in a landslide to LBJ in November.
In the whole state, Goldwater carried only a couple of rural counties.
As I remember it, throughout that campaign the only references to Goldwater and nuclear weapons I saw were those "Daisy Girl" hit-ads Johnson's campaign ran against him.
On the other hand, whatever Goldwater may, or may not have said about nukes, he was not the first one to recommend using them -- that would be Gen. Douglas MacArthur in Korea, who wanted to A-bomb the Yalu River to keep the Chi-Coms out.
It was part of why Truman fired MacArthur.
Anyway, the key point about Goldwater's views on Vietnam had nothing necessarily to do with nukes, but rather with Goldwater's insistence that we shouldn't just go fight in Vietnam, we had to have a plan to actually win the war, and Johnson never had a plan to win.
So Johnson's "Daisy Girl" adds against Goldwater successfully obscured the fact that Johnson himself had no plan to win, indeed, didn't really care about winning.
What Johnson absolutely cared about was gaining the political power to defeat Republicans, and his "Daisy Girl" ad did that for him, actually winning in Vietnam was irrelevant to him.
Anyway, that's how I remember it.
I must say, I don’t remember ever seeing that particular ad. From research I did a few years ago, I agree with your statement that Johnson did not care about winning in Vietnam. If what I saw about certain Texas companies and the Texas Book Repository Bldg. plus some things I heard this evening about the Warren Commission report on the assassination are true, then the only thing that mattered was that Johnson become president, and keep the MIC money flowing into Texas. They were probably willing to dump him for Nixon when the time came.