It would be very easy to turn it off to somewhere like Greece. There are probably only a few companies connecting to the outside world. And these are either government owned, or were until recently but are still so civil service minded and government linked that they will do as they're told.
Any commercial outfits want to keep operating in that country, so unless they think they will get a better deal from the next ruler - are also going to obey order.
California is trickier, there will be lots of links to towns in other states just because the cable run was shorter or a telco in Oregon wanted more of the market. There will also be a more complex backbone links so someone in Seattle may connect through california to Texas, so blocking out those individual routes without killing the whole network is a lot more difficult.