Quite flamboyantly, President Trump has issued a large variety of executive orders in recent days. He has fired or told to quit many staff — such as the Inspectors General, the appointed watchdogs for each agency — as well as targeted staff in selected agencies, like the U.S. Consumer Financial Protection Bureau. Thousands of probationary federal workers, who typically have been in a role for less than two years, have been fired across the government. He has also proposed to freeze agency spending, initially across the board, but then on a more targeted basis in specific agencies, like U.S. Agency for International Development (AID).
For the firings, he is largely relying on a legal theory, the unitary executive theory of government. This justification stems from the introductory words of Article II of the Constitution, which reads, "The executive Power [of the United States] shall be vested in a President of the United States of America." Advocates of this viewpoint contend that the President therefore can fire officers in the executive branch at will, without any restraint from Congress, because management of the executive branch is for him alone. The Supreme Court will need to weigh in on whether constraints are in place. However, even advocates of this view would not contend that the President is no longer responsible for carrying out a congressionally authorized program. Nor can a President unilaterally violate civil service laws created to protect federal workers from capricious or politically motivated employment actions.
For the decision to halt or delay federal spending, presently, a President can’t legally do this; the 1974 Congressional Budget and Impoundment Control Act bars a President from choosing not to spend the money that Congress has appropriated. This is part of what led to the first Trump impeachment, in which he ordered the Office of Management and Budget to withhold military aid to Ukraine as he sought to have the Ukrainian government open a criminal investigation of Joe Biden ahead of the 2000 presidential election.