Do you have cygwin on your computer? In that case, it may be that you are actually invoking the wrong
make. I once had that, took me three days to find out. This produces the exact same error message.
Apart from that, I always deem it a good idea to have MinGW installed in C:\mingw. Keep everything as simple and clear as possible (it gets complicated on its own).
One installation, and only one. No complicated pathnames, no ambiguous stuff.
Then, before you call make, you should type:
set path=C:\mingw;C:\mingw\mingw32
so there are no questions about your path, either. wxWidgets is still a hideous beast, and it can still fail to compile, but it is less likely if you have eliminated all the obvious troublemakers.