The biggest issue is that FEMA has a reputation for not delivering when it matters most (such as during Hurricane Katrina). People may have that in mind if they hear FEMA is to be involved with getting more people vaccinated and be more skeptical of the process than they already are.
Similarly, there will likely be parts of the country skeptical of the national guard, especially if they were called to help enforce law and order during the ongoing rioting. Too many people, unfortunately, equate the national Guard with heavy-handed law enforcement. President-elect Biden will have a significant uphill battle getting citizens to put that perception aside in the name of being vaccinated. I'm not optimistic he can do that (and perhaps he might not even try).
As much as I'd like to see the logistics work in terms of having the National Guard and FEMA helping out, the lack of cooperation and coordination to date between Federal, State, and Local government bodies in dealing with COVID doesn't leave many people feeling very confident that it will work especially given FEMA's mixed track record with past federal emergencies.