Yes, they can, and often do.
The black codes
Congress could pass laws about the slave market prior to the abolition of slavery in the United States. The slave trade was banned in the United States in 1808, and Congress could have passed laws regulating or outlawing the domestic slave trade before that date. However, the enactment of such laws would have been unlikely given the economic and political interests associated with slavery at the time.
The US state legislatures can pass laws applicable in their own states.
States cannot pass laws the contradict the Constitution
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Congress is not exempt from the laws they pass. Laws passed by the federal government apply to all citizens of the United States, even the people who make them.
Make law, meet with voters and help people from their states, sit on committees, pass laws.
9 out of 13
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To pass laws all states need to agree
As states are sovereign entities, they pass laws independantly of each other and hence laws will vary from state to state.
Child support is handled by the states; Congress passes laws, not the president.