How hard would it be to successfully attack (all) the Electrum backend servers? I think there is about a handful of them.
I would consider an attack successful that stops Electrum from working for a day or so.
I'm not exactly sure if this is what you're asking; nevertheless the wiki says:
It seems the storage of your keys is client-side, so if they were to get (D)DoS'd you could easily move you keys to another wallet.