I believe based on a @biobook post it makes more sense to get it very late than very early, but based on the CHEMED interview of Dr. Paul Offit (immunologist from CHOP, he’s also on the FDA vaccine approval board) less than 4 days early or late really doesn’t matter.
I don't remember saying anything like that, but I forget a lot of what I say soon after. I vaguely remember someone else quoting CDC (can't remember who it was) so I just looked it up there, and this is their advice:
https://www.cdc.gov/vaccines/covid-19/info-by-product/clinical-considerations.html"The second dose of Pfizer-BioNTech and Moderna vaccines should be administered as close to the recommended interval as possible, but not earlier than recommended (i.e., 3 weeks [Pfizer-BioNTech] or 1 month [Moderna]). However, second doses administered within a grace period of 4 days earlier than the recommended date for the second dose are still considered valid. If it is not feasible to adhere to the recommended interval and a delay in vaccination is unavoidable, the second dose of Pfizer-BioNTech and Moderna COVID-19 vaccines may be administered up to 6 weeks (42 days) after the first dose. Currently, only limited data are available on efficacy of mRNA COVID-19 vaccines administered beyond this window."
I think that they mean that these two choices (4 d earlier, up to 6 wk later) are equally good for reaching optimal antibody/immunity that will persist for a relatively long term. So if your second shot is scheduled for March 19, you could get it as soon as March 15 or as late as April 30, and your antibody levels would be equally as good in May-December, or maybe even beyond that.
But you may be more concerned about what happens in the short term, in March-April. If you want to be around people during that March15-April 30 interval, and if these are people who could potentially infect you, or people who are vulnerable and may be infected by you, that it would be better to get that second dose earlier, so that you get that boost in antibody sooner during that interval.