Most games have issues with the online servers as the game comes out and, usually, these things are fixed fairly quickly. Anybody who remembers the Metal Gear Online Beta will remember a delay of over a week before being able to play after the "grand launch" attracted far too many people.
Twisted Metal is no different, it's having some server issues that the team at Sony are rapidly trying to fix; the problems started three days ago and co-director David Jaffe has been incredibly apologetic about the whole thing:
"Thx for sticking it out with us- Twisted fans are not only bad ass sick f****, they are also- mostly!-,understanding gamers who have every right to f***ing hate us right now…so thank you!:)"
He then spent what seems like hours trying to set up a room to play with a few Twitter users and answering questions. It seems that what the team at Eat Sleep Play can do is fairly limited, this is an issue on Sony's side, but definitely expect it to be fixed sooner rather than later.