They should be held responsible for every murder committed by an illegal in their city.
I agree and every one of them who runs those cities should be arrested for failing to carry out Fed law.
Let their sorry asses land in jail and see how long they remain a sanctuary city.
The job you describe is one mandated to US Marshall's. Arresting aliens who have overstayed their allotted time or those who crossed the border without legal authority will be detained in Federal Custody, Usually space rented from local agencies where overcrowding is a problem.
If Trump wants to round them all up, he will need to find space to detain them, increase the number of US Marshals, hire more US Deputy Attorneys to prosecute them, and pay private Council or Public Defenders to defend their right to due process, and hire more Administrative Law Judges to conduct Hearings, plus clerks, court reporters and bailiffs.
You people on the right want your cake and eat it too. That can't happen, you can't have smaller government and cut taxes, and elect a person who will expand government and cut taxes ... well you can, you elected G. W. Bush twice.