AFAIK, their salaries and staffs operate within an executive budget authorized by Congress. If not, Congress has the power to trim the money. IIRC, Congress toyed with the subject of making it illegal to use allocated funds to pay for czars. I assume that never got past the talking stage.
Anyway, those funds are a drop in the bucket. The difference between Congressionally mandated spending and the Congressionally mandated debt limit is Medicate, Medicaid, Defense, Social Security, and entitlements, mostly, with some amount in maintaining regulatory and judicial activity, plus foreign aid.
I'm not giving Obama a pass, by any means - just asserting that Congress created the debt, deficit and spending issues. Under the Constitution, spending and borrowing is a Congressional function.