The central principle which the lawsuit seems to be attempting to remedy is the erosion of the ‘Separation of Powers’ doctrine which has been substantially undermined by the Obama White House. John Boehner the Republican House Speaker from Ohio is the leading force behind the considered lawsuit. However, the alliances most certainly extend to the Tea Party as the issue at hand is a key grass roots Tea Party complaint.
The reason for suing as opposed to laying out Articles Of Impeachment seem to be grounded in politics. Namely, the GOP likely doesn’t want to be perceived as personally attacking Obama. Impeachment in essence is a Federal charge rising to the level of ‘High Crimes and Misdemeanors’ whereas as a lawsuit is a simply a complaint among parties.
To my knowledge and understanding a sitting President has never been sued besides Obama. The likely result of the lawsuit is impossible to predict because the case could be deemed ‘A Political Question’ case for which judicial relief cannot be granted because there is no authority for review. Conservative George Will, however, has stated “Congress does have the power under the Constitution to define the jurisdiction of the federal courts. Within that power, Congress could just pass a law declaring that the House or some of the members of Congress has a right to sue the President over a legitimate inter-branch dispute.”