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The "Department of Government Efficiency" isn't actually a department since those can only be established or disbanded by Congress. So Musk isn't going to have the kind of power that a department head would.

Trump said it'll operate outside of government, so basically be a federal advisory committee of which there's already tons.

And who knows what Musk will do when he runs up against the ethics requirements for those committees, he gets tons of govt $$ and his companies interact with a lot of federal agencies.

In the end all they can do is make suggestions, Congress decides how much money get spent and on what.

EDIT: That said influence is different.. actual heads of actual departments can adopt suggestions by Musk to remove limits on killing animals to launch more rockets or dump waste to make more batteries etc..