I'm actually surprised at how low the actual vaccine acceptance is and how slowly more people are getting vaccinated at this point.  From the polls posted, it was foretold that 20% were pretty adamantly against getting a shot and that 10% more would need convincing/prodding.  However, we've reached a point where almost 40% haven't gotten a shot.
I think that two things weren't anticipated.  First is (and I am very surprised) how few people under 35 want to go get vaccinated.  Second is the damage done by the unnecessary pause of J&J.  That gave ammunition to anti-vaxxers and put more fear into people who were on the fence.  That pause may have been the worst decision made in the whole pandemic to be honest.
Honestly, I think what should be done now is to have both insurance companies and the Government say that if you aren't vaccinated and you get COVID-19, you aren't covered at all.  As long as you get the first shot, you are covered.  Companies also need to have a policy that if you choose not to be vaccinated and miss work due to COVID-19 you do not get paid while if you are vaccinated you will be paid.
At the current rate, there's very little chance to hit the 70% of adults by 7/4.  Honestly, I'm not sure if it will ever get hit if something drastic like my suggestion isn't done.