Actually Cynthia Coffman is not supporting this lawsuit, they are appointing a special attorney general.  What is significant is the demonstrated lack of concern for our representative process by our elected representatives.  Our country is devolving into disparate groups of activists and our elected officials conduct themselves as if they have no ability to lobby their federal representatives. They don't have a valid argument, no rights will be violated and Trump probably has more right to rescind this action than Obama did in implementing it. This is a constitutional issue and no president has the authority to override constitutional law.