It probably wouldn't be
that bad: there's already copyright doctrines for situations where something is so commonly used that it can't be protected, or where there's only one reasonable way to express a particular idea. Plus, copyright protection is usually not extended to extremely short phrases or snippets of text, so even in an "APIs are copyrightable" world, "parse(string)" is probably OK. (Of course, I only said
probably, which is part of the problem.)
The Oracle argument (and as things currently stand in their case, the accepted argument) is basically that the API taken as a whole can be protected even if each individual function name can't, so you could protect the "Java API" but not "compare(a, b)". The idea of copyright arising from "structure, sequence and organization" is well established in the computing context as well as others (for example, you can hold copyright in a compilation even if the individual things being compiled aren't themselves copyrightable).
Still, API copyright would lead to all sorts of uncertainty at least at first, and certainly puts compatible implementations or reimplementations in the crosshairs, so I'd really prefer an Oracle loss here.