To my understanding, that's correct. The R0 of the initial strain was somewhere around 2-3. For every infected individual, 2-3 additional individuals were infected. For the delta variant, R0 is around 8-9. In order to get herd immunity, `R0 * vaccination_rate * vaccine_effectiveness` must be less than 1. Even if a new vaccine can reach the same 95% rate as the original vaccine had on the original strain, the increase of R0 raises the necessary vaccination rate from ~65% to ~85%.
That's not to say that it's impossible. Chicken pox has a similar R0, but universal vaccination has greatly decreased the spread of the disease. At this point, it mainly occurs in small pockets of non-vaccination, and cannot spread significantly into the wider population. But that requires education and popular support, and is where we'll need to focus our efforts next.
[0] https://www.cnn.com/2021/07/29/politics/cdc-masks-covid-19-i...