Not customers suing, but shareholders. Tesla now has probably over 1000 people with pre-MVPA paperwork giving them a month for expected delivery. Those pre-MVPAs have language allowing Tesla to postpone delivery, so nothing customers can do.
But, if Tesla has known for some time that they will be unable to deliver those vehicles, and the subsequent delay leads to enough negative publicity regarding Tesla that the stock drops, shareholders can try to make a claim against Tesla for "hiding" material information, and their actions led to them losing money. It's basic corporate governance -- get any bad news out as quickly as possible. That's why any time a company thinks it won't hit it's earnings guidance it announces that mid-quarter.
I'm not suggesting this will happen, but the mere possibility actually says to me that the panic around delivers being uniformly delayed is very possibly exaggerated. I would expect a company like Teslamotorsclub if they knew deliveries were going to be late, to tell customers that once they knew. Telling people at the past minute will only make things worse, and that's not their style at all.