The first thing you need to do is make sure you have IO::Socket::SSL installed. It is a prerequisite for Net::Twitter::Stream, but it isn't listed in the Makefile.PL, so it may not have been installed. There are a couple several year old bugs on this for this module.

After checking that, it's time to deal with Net::Twitter::Stream. It has some serious issues. Generally, with system calls, you want to be checking return values and $!. If they are undef or 0 where something useful should be returned, checking $! is essential to get the error back. Net::Twitter::Stream doesn't check for errors and return them to the code calling it in a way that can be useful. Basically, you're screwed. If there is a better alternative module, I'd suggest switching to it.

  rsync -avz rsync://public.activestate.com/perl-current/ .
  ./Configure -des -Dusedevel -Dprefix=/path/to/test/perl
  make test
  make install

perlbug at perl.org