Is the question whether Obama would order some kinetic response to the Chinese firing?
He would know about it after the fact.
The only question is: Will he allow the US Navy to do what it has done for over 200 years to assert freedom of navigation?
Obama has shown considerable deference to the USN in these matters.
Twice battle groups have sailed "provocatively" into the Yellow Sea while he has been in office.
I don't think Obama wants a showdown with the defense establishment over these matters. He's used up all that capital with the homo thing.
you say that as though his goals are liberal ones.