Since President Obama, the Executive, is refusing to protect the United States from an invasion, and the Judiciary wields no enforcement or military power, Article IV, Section 4 of the United States Constitution demands that the federal Government defends this Nation from both foreign and domestic invasion.
Since neither the Executive Branch is willing to honor their Oath to the Constitution under Article IV, Section 4, and since the Judiciary has no method of honoring that clause of Article IV, Section 4, the only remaining branch of the Federal Government that is both capable and empowered to repel the foreign invaders is the Legislature:
Article 1, Section 7:
To provide for calling forth the militia to execute the laws of the union, suppress insurrections and repel invasions;
To provide for organizing, arming, and disciplining, the militia, and for governing such part of them as may be employed in the service of the United States, reserving to the states respectively, the appointment of the officers, and the authority of training the militia according to the discipline prescribed by Congress.
Congress does not need Obama's approval to act against this invasion.
Obama would then be compelled by Article II, Section 2, to repel the invasion identified by Congress:
The President shall be commander in chief of the Army and Navy of the United States, and of the militia of the several states, when called into the actual service of the United States.
If he refuses to do so, Impeachment would not only be right, but a duty.
Anyone that provided aid and comfort to the invaders would be guilty of Treason via Article 3, Section 3 and summarily executed without delay:
Article III, Section 3:
Congress has the power under Article 1, Section 9 to suspend Habeas Corpus during an invasion of US soil, this would allow to Constitutionally detain and restrain US citizens who aided, abetted and provided comfort to the invaders, but not in a heinous enough fashion as to execute them. Eighth Amendment protections against torture would still apply.
The privilege of the writ of habeas corpus shall not be suspended, unless when in cases of rebellion or invasion the public safety may require it.
Eight Amendment:
Excessive bail shall not be required, nor excessive fines imposed, nor cruel and unusual punishments inflicted.
