When someone protests an action on the part of the government by saying, "That's vile! That's wrong! That's downright unconstitutional!," they're saying that the action violates the tenets of the U.S. Constitution.
The U.S. Constitution is our nation's founding document, laying out a structure for the executive, judicial, and legislative powers, and assigning to people specific rights, such privacy, free speech, and voting. Violations of the Constitution are the highest forms of illegality in our nation, though famously hard to nail down.