before one of these variants fully overcomes the vaccine

First of all, there isn't a "the vaccine." There are two different vaccines that function similarly, and there are two more coming that have completely different methods of action. Second, the two that are out right now target the spike protein. That's the protein that the virus uses to interface with the human body. If that spike protein changes so much that vaccine induced antibodies can't detect it, it's unlikely- possible but unlikely- that the virus would still be able to interface with humans as effectively as the one we've been dealing with this past year.

It's been speculated that this is what happened with the infamous cluster five mink strain. The virus adapted to spread wildly in minks, and the very few humans that got it- almost all of whom worked with minks eight hours out of the day- didn't seem to have an effective immune response. But since the virus evolved to spread in minks, it wasn't good at spreading in humans.

It's entirely possible this thing does evolve to a vaccine evading extent, and it's possible we'll need an annual shot for it like we get for the flu, maybe with the two even being combined eventually like the MMR vaccine, but for now? The immediate future? It just doesn't seem like something that could happen imminently. The correct precautions should be taken and genomes should be sequenced as much as possible, but it really isn't worth panicking over right now. The evidence just isn't on the side of fear right now.