Yes, drill again. If it becomes a large oval hole (instead of two holes near each other), you can sometimes insert something like matches/toothpicks to make the hole a bit tighter so the plug fits.
You can also apply some mounting glue in the hole if you're unsure. Exactly how you should do it also depends a bit on the load: is it a kitchen cabinet or a lightweight picture frame you're putting up, requiring different solutions to make it good