Anti-Federalists objected to the necessary and proper clause because they believed it could be used by the federal government to expand its powers, and they objected to the supremacy clause because they felt it granted too much power to the federal government at the expense of the states.
Anti-Federalists objected to the necessary and proper clause because they believed it gave too much power to the federal government and allowed for potential abuse, while they also opposed the supremacy clause because they felt it undermined the authority of state governments.