The Moderna and Pfizer vaccine induces something called a polyclonal response. Basically, the vaccine instructs the body to generate numerous shaped antibodies that can connect to many different parts of the virus (see picture). Those antibodies are diverse in shape and cover the whole waterfront of the spike protein.
A spike protein mutation here and there would still leave areas for the antibodies to attach. Mutations to those target sites raise the possibility that the vaccines would be less effective, not necessary that they won’t work at all. Mutations are likely a long way from making any vaccine useless. Scientists say it will probably take years.
However, if a random mutation did render a vaccine useless, the mRNA instructions are incredibly easy to change. This is the beauty of this type of vaccine. It’s like editing a Word document; just tweaking the code a little. And, the FDA wouldn’t need Phase I-III trials again. This is because the code isn’t changed enough to concern safety or efficacy. They would just need to see a study with a few dozen people that showed the new code produced satisfactory amounts of antibodies and protection against the mutated virus.
According to GISAID (a public genetic database of the virus) there’s about 12,000 known mutations for the COVID-19 virus. And the mutations in a few (UK, SA, Brazil, and Nigerian variants) look like they change some of the target sites, but certainly not all.
We are still very much hopeful for the effectiveness of the vaccines.
Some data sources for more reading:
WHO 12,000: https://www.who.int/publications/m/item/weekly-epidemiological-update—5-january-2021