Specifically, I meant that the constitution explicitly gives each of the Army and the Navy cabinet-level power and responsibility. The Air Force was given the same power and responsibility, without amending the constitution.

That's not a very good example. The Cabinet consists of the heads of various Departments, whichever ones the President wants to hear from at any given moment. The Departments are created by Congress.

An Amendment wasn't required to create the Air Force any more than it was required to create the DHS, or is required to create any other Federal agency. Congress has the power to create, destroy, and reorganize Federal agencies as it wants to. So in 1947, Congress created the Department of Defense as a Federal Department, which the Constitution allows them to do, and put the Army, Navy, and Air Force (new) under it. There wasn't anything even vaguely unconstitutional about it, even taking a really uncharitable reading.

Congress creates new Departments fairly regularly; there wasn't a need to go through the amendment process for the DoD any more than there was to create the Departments of State, Transportation, Energy, Labor, Education... etc. All it takes to create one is the same process to pass any other piece of legislation.

I would personally not be against requiring an amendment to create new agencies, just on the grounds of controlling governmental scope creep, but that's not the way things are set up. Congress has been creating Departments since the ink was barely dry on the Constitution itself.

Actually, I think I agree with you. They should change the org-chart and put the AF back under the Army.

I still don't understand your comparison to Obamacare. Are you asserting that the constitution would authorize Obamacare with some tweaks to heirerarchy? Please explain.

Nope, I was just comparing the magnitude of the changes, not really the structure.

How is the magnitude comparable? Obamacare is not authorized by the constitution at all - to become constitutional, it would need to be eliminated. To become constitutional, the Air Force would need one arrow in the org chart to be changed.

I don't see the changes as being remotely comparable in magnitude.