According to an AARP newsletter of a couple of weeks ago, the outer time limit is six weeks:
Second dose timing. The second dose of either the Pfizer-BioNTech or Moderna vaccine may be scheduled for up to six weeks after the first shot, according to an update posted by the CDC. When the FDA authorized the two vaccines for emergency use late last year, it said that the second dose of the Pfizer vaccine should be administered in 21 days while the Moderna protocol is for the second shot to be given in 28 days. CDC still says that while the “second dose should be administered as close to the recommended interval as possible,” if that is not feasible the second dose can be received up to 42 days after the first one.
Here is the link to that article:
What You Should Know About A COVID-19 Vaccine