The makers of two of the vaccines have stated they'll have 1,000,000,000 does available by April. That would seem to mean that (hopefully) it will be available to the general public earlier....
1) That's the figure worldwide. The number available in the U.S. will obviously be much lower;
2) For all of the vaccines that will be available on this time frame, each individual needs two doses, so cut that number in half;
3) The second dose is administered 3-4 weeks (depending upon the specific vaccine) after the first, so it will be almost a month after a dose becomes available for an individual before they can considered to be protected;
4) The bulk of that 1 billion figure is the AstraZeneca vaccine. The problem is that the third stage trial data for this vaccine is . . . weird, to the point that the whole trial may end up needing to be redone. They had a manufacturing glitch that caused some of the trial subjects to only get a first dose of half strength. Then, that small and
extremely unrepresentative sample showed much higher resistance to the virus. There is a reason why a half strength first dose could actually be better, but the way that the results came about are tainted. They're still trying to sort out whether or not they can move forward yet;
5) The other two vaccines seeking approval are difficult to transport and store. The Moderna vaccine needs to be kept at -30 Fahrenheit; the one from Pfizer at -110 F. There aren't a whole lot of places that have freezers that can reach -110 degrees. So distributing these vaccines is going to be expensive and difficult, and the ongoing chaos of the federal government's "plan" for the vaccination process isn't helping.
6) Just in general, don't take a drug company's press release at face value. For instance, the number that Pfizer has given for how many doses they can manufacture should be taken literally: that's how many doses they are capable of manufacturing. It turns out that the supply chain won't be able to supply enough ingredients to actually make that many doses.
It's going to be at least six months before most of the population has been inoculated.