According to a chart on NPR, the rate of administration of the drug peaked in the first 10 days of April, and the daily injection rate is declining at the same rate it took to reach the peak in early April. (Look at the second chart on that page). During that peak, about 33-35% of the population had gotten at least one shot,
according to this graph here.
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If you expect the rate to decline at the same rate it went up, and so far that is what it is doing, so that the downhill side of that slope is practically like a mirror image of the uphill side, that will give us a
final outcome of maybe 60-70% of the population injected by the time they reach a saturation point.
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This is highly speculative, and there is not much reason to expect the results to continue the way they have, but extrapolating into the future that's what we're looking at right now.