Many places are now asking for more shots and state they can get them into arms if they had the shots. So it looks like it has started to move more into a production question. I am assuming that the latest lack of shots is due to production and not distribution constraints.
I do wonder about whether companies are doing all they can to increase production. For a company if they invest capital into manufacturing and the vaccine is too effective in reducing the virus in the world. They may have too much invested for a good return. But I think that given the rate of mutations they will have a market for a while. In any case, if they are hesitant to build more production capability then perhaps the government should invest in it. Especially if the production capability can repurposed if a new virus becomes a threat. Manufacturing supply chain is another area, if it is restricting production, that could be helped (DPA, capital, etc.).
USA has enough shots on order to cover its needs, so the value to invest in even more production may not be there. But I rather spend a little too much in a pandemic than to be optimal in economics.