I feel like "in a few months" and "I have no idea" can see A LOT of overlaps, with how some places have been doing their rollout. In the US there should be enough to cover everyone, but will there be enough people to actually administer the first dose to "every American adult" by the end of May, without appointments being constantly full every day? I hope so, but some locations have been very messy.
So I'm hopeful, but I'm somewhere in between "in a few months" and "I have no idea", since I'm not old or in medical/education/agriculture work, so I mean, whenever the other tiers comes up, then yes. "Severe medical problems" only starts in a week or so, so that will also need to go through before any other tier.