Washington the state is the state, not the president, nor the city. Considering the president is dead and the city got destroyed by a nuclear weapon on January 20, 2013 in the events described in the opening cutscene, it can be safely assumed you're here to read about the state.
Washington state never actually seceded from the United States, although many other states did. Like the other member states of Pacifica, it was forced to fend for itself as the Union fell apart between January 2013 and 2014. It joined the defensive pact that became Pacifica.