BOSTON (SHNS) – A court date has been set in the showdown over sheltering migrants.

Suffolk Superior Court on Tuesday will be the setting as plaintiffs seek a temporary restraining order to force compliance with the state’s right-to-shelter law.

Lawyers for Civil Rights Boston filed the lawsuit on Friday against the Healey administration, on behalf of three families who the organization said are “on the brink of homelessness.” The suit comes after Gov. Maura Healey announced this month that the state could no longer guarantee housing for families and pregnant women, despite a state law that guarantees housing for qualifying families.

The hearing will be held hours before Nov. 1, the date that Healey determined the state’s shelter system would “reach capacity” and that families may begin to be placed on a waiting list if there is no room available.

The governor said that starting Wednesday the state would not add any new shelter units and families who come seeking housing would be assessed, and those with higher needs would be prioritized for placement.

Lawyers for Civil Rights alleges that these are “proposed changes to the Right-to-Shelter law,” by” imposing an artificial ‘cap’ on the total number of shelter spaces and units the State will provide to homeless families” and by “creating a ‘waiting list’ for families eligible for emergency shelter.”

The organization is calling for the temporary restraining order to stop the state from “undermining” the right-to-shelter law, until the Executive Office of Housing and Livable Communities gives the Legislature 90 days notice of changes to the emergency shelter program, giving lawmakers a chance to “evaluate and potentially prevent the changes,” which LCR says is required in the law.

Judge Debra Squires-Lee will preside over the hearing, scheduled for 2:30 p.m. in Boston.