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When anyone else or any other organization declares a law unconstitutional, then that's nice, nice to have their opinion, but mostly that's just their opinion. As I recall, the president is sworn to uphold the laws. If there is some law the president refuses to enforce, then there might be a law suit that goes to the Supreme Court. Or there might be an impeachment proceeding in the Congress.
Really, in practice there is a lot of discretion on what laws get enforced, and part of the role of the Attorney General (AG) is to decide, as a political matter as the AG serves at the pleasure of the president, what laws will be enforced. Still, likely (I'm not a lawyer) if I am suffering because some law was not enforced, then I can bring suit against the people supposed to enforce that law.