Aside from the problems with training 300M people to use a mask (and guaranteed, most people won't wear them properly - a properly fitting mask is uncomfortable), it's not just "1" mask, it's at least one mask a day.
So to cover the USA for 10 days, that's 3 billion masks. There aren't that many masks available.
In shortage situations, one mask reused properly is better than no mask.
I work at a medical center in Korea and we are under the following instructions:
1. Place masks for reuse in a specific place to avoid cross contamination.
2. Treat the outside of the mask as contaminated. Don't touch.
3. Wash hands after wearing a reused mask.
4. Throw out masks if they get wet, damaged, or (N95 only) folded.
I was assuming an N95 respirator and some sources say they can be used for a workday as long as they haven't become contaminated from direct exposure to bodily fluids -- there's no point in equipping the country with surgical masks since they won't offer any significant protection from the virus anyway.
So to cover the USA for 10 days, that's 3 billion masks. There aren't that many masks available.