I can see why the Johnson Campaign's Daisy was controversial. I also know that Johnson won the 1964 United States presidential election. However, how much of a political impact did Daisy really have? Wikipedia tells me "Jack Valenti, who served as a special assistant to Johnson, later suggested that pulling the ad was a calculated move, arguing that "it showed a certain gallantry on the part of the Johnson campaign to withdraw the ad."" This doesn't make clear the real implications and seems hypothetical.
The sentence right before the one you quote in the wiki article is instructive:
The ad was immediately pulled, but the point was made, appearing on the nightly news and on conversation programs in its entirety.
The commercial became widely known and seen because ABC News and CBS Nightly News broadcast it a lot due to the controversial content, and the nature of the content makes it hard to not form some kind of an opinion on it.
In other words, the impact was widespread awareness of the ad and the controversy.
To make this a tiny bit more relatable: consider the uproar whenever Trump or someone in his team make a controversial tweet or statement. For instance, the frenzy that erupted when Kirstjen Nielsen falsely blamed Congress and the courts for the Trump administration's policy of child separation.