Wish I could find estimates showing “At current / projected vaccination rates it will take X years to vaccinate 90% of the population”, per country. I heard on TWiV (This Week in Virology podcast) for the US it was ~6.6 years and I believe it was based on < 90% of pop.
I hope so. But, frankly, most national and local responses to this outbreak have been subpar. I do not take it for granted that we (the US) can pull off this major logistical challenge smoothly or on an aggressive timeline.
New vaccines will likely be approved over the next few weeks (particularly the Oxford one), greatly increasing supply, and the kinks around distribution and administration will be slowly worked out (the Oxford one will also reduce the logistical challenges there; no special transport or storage needed). I'd be very surprised if rates don't go up considerably within a month.