Prof. Steve Vladeck (One First) discusses the Administration's plan to send Texas National Guard troops (unfederalized, so under the command of the Texas government) to Chicago and the potential statutory and constitutional problems with this plan. He also discusses how Illinois might challenge this in court, including by suing Texas in an original jurisdiction action in SCOTUS or by suing the Secretary of Defense in district court. Consider that there should be two automatic votes (Thomas and Alito) to allow the action.
Although he does not discuss it, there is a third option--sue the U.S. in SCOTUS on original jurisdiction. The case arguably raises some of the sovereignty and speed concerns that justified original jurisdiction in South Carolina v. Katzenbach.