During a Facebook Live interview yesterday with the Seattle Times, new Seattle Mayor Jenny Durkan was asked about the decisive ruling by King County Superior Court Judge John Ruhl declaring the Seattle income tax illegal. Durkan was asked if she thought Seattle should appeal the court loss. Saying she needed to meet with the City Attorney and actually review the ruling before making a final decision, Durkan still said the case should be appealed though it was a "long shot" due to restrictions in state law and state constitution. 

On that point, Durkan said (21:39 of video):

"My guess is, as I said on the campaign, I think it's a long shot. I think that under the current state of the law – both the state law that prohibits cities from imposing income taxes as well as the constitutional provisions – will strike down our income tax law, but I think we have to find the answer to it." 

We'll have to see what happens next but I think the answer she is looking for can be found in this one-page income tax ruling from the state Supreme Court in 1960 (in-part): 

"The argument is again pressed upon us that these cases were wrongly decided. The court is unwilling, however, to recede from the position announced in its repeated decisions. Among other things, the attorney general urges that the result should now be different because the state is confronted with a financial crisis. If so, the constitution may be amended by vote of the people."

Imagine that? The way to change the constitution is through a constitutional amendment with approval from the sovereigns of the state. 

Additional Information
Seattle income tax may not make it to Supreme Court
Timeless advice from WA Supreme Court on income taxes