Won't really matter. J&J is behind on production... a quick approval wouldn't lead to a huge release of vaccine supply. Supposedly, they will have under 10 million doses ready by the end of the month. So an extra week or 2 will just give them a chance to build up a bit more inventory.
We are at 1.3 million shots per day in the US... Just the addition of J&J, 10-20 million per month, will get that up to 1.6-1.9 million per day, by mid March with the J&J only requiring one dose. At that pace, we should have a large portion of the population vaccinated by July. Maybe not enough to get rid of Covid, but enough to make a big difference. There is a good chance we will be able to add additional vaccines (AstraZeneca and/or Novavax) by April... hopefully pushing us over 2.5 million shots per day by May.
At some point, the issue won't be lack of vaccines -- It will be too many anti-vaxxers refusing to get the vaccine. I don't know when we will get to that point, or what percentage of the population it will be. But it wouldn't surprise me if by June/July, we get 50-60% of the adult population vaccinated, with the remainder hesitant to get the vaccine.