Often part of disputing the constitutionality of a law is requesting that the court considering it also temporarily put its enforcement on hold, as I understand

Often part of disputing the constitutionality of a law is requesting that the court considering it also temporarily put its enforcement on hold, as I understand it. If the court chooses to (and in a case where a law that was already basically ruled unconstitutional has been passed again, one assumes it would so choose), that law is simply ineffective until a final ruling is obtained. Naturally, you can appeal the decision to hold the law's enforcement, but the law is on hold unless and until a higher court overturns it.