Our A320's our currently only 1 hour ETOPS certified which precludes trans-atlantic flying. There is an airline in Australia the has 2-hour ETOPS 320's and does trans-oceanic so it is possible. I think it wouldn't take much more than a second HF radio and some $$ for certification.

The Navy uses 737's and C-9's (extended range) to cross the pond. Usually stop in Canada or Lajes. No reason an A320 couldn't do the - at least east bound. How about Europe to Reykjavik to the states?