Just so everyone knows - they are aware of the issues. The following was posted 3 hours ago on their Facebook page.
"For all those having connection issues, folks are working around the clock to resolve the issues. It seems if you're persistent you may be able to log in. Sorry for the inconvenience and hassles!"
Though it doesn't give any information as to why, or when, it at least lets us know they are aware of it and are working to correct it.
I tried it and it took two times to connect. Not too bad. Also, having finished the campaign and some "Death Mode" levels, this game looks like a pretty easy platinum (2 really ).
Edit: Well I finished and synched it. I think it counts as 2 platinums but when I look at my trophies on the website (us.playstation.com) it only counted as 1 platinum (13 total for me). On the PS3 it shows 1 more (14 total).