No governmental entity under the control of two volunteer billionaires and lacking statutory authorization can be a real “department.” It will operate as a small office in the executive branch. Given the identity of the two billionaires, however, it is completely possible that it could recommend enormous cuts in federal spending–Project 2025 on steroids. Then what?
There will be a willing audience for this kind of counterrevolution in Congress, most notably in the House. The GOP is going to have tiny and unreliable majorities in both houses, however. Are the moderates really going to swallow enormous cuts that will cause massive pain to their constituents and put their seats in jeopardy at a time when the economy is actually running quite well?
History says no, but history is not always a reliable guide.