Dozens of cities have filed briefs backing Boise’s position, saying that they are confused as to how broadly the Ninth Circuit ruling applies and that the decision has impeded enforcement of basic health and safety laws. In some cases, the cities contend, the decision has actually made it harder to build housing meant for the homeless.

Among Boise’s allies is Los Angeles, which has passed more than $1 billion in bonds for permanent supportive housing but has found steep neighborhood resistance. Mike Feuer, the Los Angeles city attorney, said the Ninth Circuit decision raised as many questions as it answered. For instance, to determine whether or not it is in compliance with the ruling, does the city have to constantly count how many beds there are and compare it to the homeless population? Can Los Angeles prohibit sleeping in sensitive locations, such as next to new homeless shelters?

“The language, rather than citing clear principles where constitutional questions are at stake, makes local jurisdictions vulnerable to lawsuits as they struggle to achieve a balance between the legitimate rights and interests of homeless people and the legitimate rights and interests of other residents and businesses,” he said.

Whatever happens in the Boise mayor’s race, Boise v. Martin is far enough along that its fate now rests with the Supreme Court: Even if she is elected mayor, Ms. McLean said, she has no plans to withdraw from the case. “The case is moving forward — that ship has sailed,” she said. “I just still maintain that we can do this without ticketing folks and moving them into the criminal justice system, which will make it harder to find shelter, home and work.”