CDC never said that herd immunity isn't going to happen. A former CDC director was in the news saying that he worried that slowing vaccination rates might mean that herd immunity will be elusive.
There have been several other credible experts who have shared this opinion recently. I think it is a mistake in public health messaging to be publicly making these statements. It gives the anti-vaxxers ammunition and let's them say "see, there is no point in getting the vax because we will never reach herd immunity."
Polling has shown that about 25-30% say they will not get vaccinated. That number is probably higher than reality because a lot of people are going to have to get vaccinated for work and travel and given in to demands from family to get vaxxed in order to resume in person visits, etc. Real world data is currently showing that COVID 19 rates drop like a stone when vaccination rates hit 60%. That is probably the herd immunity threshold and it may be lower than expected due to very high efficacy. So, getting to 70-80% vaccinated may be what is necessary to get to practical elimination where, like measles, COVID is effectively gone except for the occasional outbreak in an anti-vaxxer community.