"The Republican lawmaker said Thursday that she is “drafting a Declaration of War against the Mexican cartels,” even though... the Constitution only permits declarations of war against actual nations."
I see no such limitation in the Constitution, which merely says "The Congress shall have Power ... To declare War, grant Letters of Marque and Reprisal, and make Rules concerning Captures on Land and Water;"
There is no limitation there.
Granted, it's a stupid idea, and certainly not what the Framers had in mind, but if Congress was to declare war against cartels, who exactly could stop them?
But keep in mind that for a politician, having success with a policy is much less valuable than just appearing to be doing something about bad thing X.