Final answer:
The Office of Management and Budget (OMB) is responsible for supervising the federal budget's preparation and advising the President on budgetary issues.
Step-by-step explanation:
The entity responsible for supervising preparation of the federal budget and advising the President on budgetary matters is the Office of Management and Budget (OMB). This office operates within the Executive Office of the President and is tasked with producing the President's budget, overseeing its implementation, and managing the executive bureaucracy. Its extensive responsibilities include advising the President on the actions of various executive departments and agencies, overseeing performance levels of bureaucracies, and coordinating and reviewing federal regulations for the President.