I remember GitHub had something like what Mike M suggested for their search. I just noticed that it's changed, and what they do now is make the selection a part of their autocomplete-like menu:
[![enter image description here][1]][1]

I imagine the default selection at the top is what they believe to be the most common, which makes sense to search in the current repo by default. An advantage I note in this is that it let's you switch without hassle. If I wanted to search "rails" in "All GitHub" (which makes more sense), all I need to do is press <kbd>↓</kbd> before hitting <kbd>Enter</kbd>

  [1]: https://i.sstatic.net/noLWx.png