President Obama and Arizona Governor Jan Brewer were both claiming victory Monday, but in Brewer’s case it’s hard to see why. The US Supreme Court struck down three provisions of Arizona’s controversial law on illegal immigration — a law that Obama opposed and Brewer signed — because they infringed upon the federal government’s sole authority over such matters. “Congress has occupied the field,” Justice Anthony Kennedy declares at one point. The most contentious provision, meanwhile, was a rule instructing police to verify the immigration status of everyone they stop. It survived the court’s scrutiny, but on somewhat technical grounds: A lower court had enjoined the provision, so it was too early to assess whether it would prove constitutional in practice.

Yet in largely upholding Congress’s monopoly over immigration matters, the high court also underscored the legislative branch’s utter failure to deal with a vexing policy issue of profound importance to all Americans — and particularly to border states like Arizona. A key reason Arizona’s law passed to begin with is the disconnect between the letter of federal immigration law and a reality in which millions of illegal workers remain in the country and form a crucial part of the labor force. Since Congress occupies this field, it also has a responsibility not to ignore it.