What about the fact that the Congress (NOT the Executive) is only authorized to bring military force into the states to suppress insurrections at the invitation of the Governor or Legislature of the state? None of the Confederate states requested that either Lincoln or the Congress send in an army to assist them, did they?
Art I, Sec 8: [Congress shall have the power...] To provide for calling forth the Militia to execute the Laws of the Union, suppress Insurrections and repel Invasions;
Art IV, Sec 4: The United States shall guarantee to every State in this Union a Republican Form of Government, and shall protect each of them against Invasion; and on Application of the Legislature, or of the Executive (when the Legislature cannot be convened), against domestic Violence.
(There is an absolute right to repel Invasion, but nobody's seriously suggesting the Confederacy invaded itself, are they?)
The Militia Acts of 1792 and 1795 gave the president the power. Section two states "That whenever the laws of the United States shall be opposed or the execution thereof obstructed, in any state, by combinations too powerful to be suppressed by the ordinary course of judicial proceedings, or by the powers vested in the marshals by this act, the same being notified to the President of the United States, by an associate justice or the district judge, it shall be lawful for the President of the United States to call forth the militia of such state to suppress such combinations, and to cause the laws to be duly executed. And if the militia of a state, where such combinations may happen, shall refuse, or be insufficient to suppress the same, it shall be lawful for the President, if the legislature of the United States be not in session, to call forth and employ such numbers of the militia of any other state or states most convenient thereto, as may be necessary, and the use of militia, so to be called forth, may be continued, if necessary, until the expiration of thirty days after the commencement of the ensuing session. "