Oh, look at Adrian, doing it "right".
I pretty much agree with CatBrat - if that crack is really going to be a problem, then filling its existing dimensions with ANYTHING isn't going to help you when it spreads and actually becomes a concern later.
OTOH, the other thing that came to mind is Laticrete epoxy grout. You can get it at Lowe's. Minimum buy-in is probably $20-25. You mix the two-part liquid and then add their dry mixture to it. Open time is about 30-40 minutes, but during that time, it works just like regular tile grout, so you can probably jam it into that crack pretty easily with a rubber grout float. When it dries, it's waterproof and about 3000 janka.
