No need to split the country in two. Just run it the way it's supposed to run. The federal government deals with things that effect the country as a whole. These are enumerated in Article one, section 8 of the Constitution:
To borrow Money on the credit of the United States;
To regulate Commerce with foreign Nations, and among the several States, and with the Indian Tribes;
To establish an uniform Rule of Naturalization, and uniform Laws on the subject of Bankruptcies throughout the United States;
To coin Money, regulate the Value thereof, and of foreign Coin, and fix the Standard of Weights and Measures;
To provide for the Punishment of counterfeiting the Securities and current Coin of the United States;
To establish Post Offices and post Roads;
To promote the Progress of Science and useful Arts, by securing for
limited Times to Authors and Inventors the exclusive Right to their
respective Writings and Discoveries;
To constitute Tribunals inferior to the supreme Court;
To define and punish Piracies and Felonies committed on the high Seas, and Offences against the Law of Nations;
To declare War, grant Letters of Marque and Reprisal, and make Rules concerning Captures on Land and Water;
To raise and support Armies, but no Appropriation of Money to that Use shall be for a longer Term than two Years;
To provide and maintain a Navy;
To make Rules for the Government and Regulation of the land and naval Forces;
To provide for calling forth the Militia to execute the Laws of the Union, suppress Insurrections and repel Invasions;
To provide for organizing, arming, and disciplining, the Militia, and
for governing such Part of them as may be employed in the Service of
the United States, reserving to the States respectively, the Appointment
of the Officers, and the Authority of training the Militia according to
the discipline prescribed by Congress;
To exercise exclusive Legislation in all Cases whatsoever, over such
District (not exceeding ten Miles square) as may, by Cession of
particular States, and the Acceptance of Congress, become the Seat of
the Government of the United States, and to exercise like Authority over
all Places purchased by the Consent of the Legislature of the State in
which the Same shall be, for the Erection of Forts, Magazines, Arsenals,
dock-Yards, and other needful Buildings;—And
To make all Laws which shall be necessary and proper for carrying
into Execution the foregoing Powers, and all other Powers vested by this
Constitution in the Government of the United States, or in any
Department or Officer thereof.
Everything else is left to state and local governments. In this scenario New York and Mississippi can deal with their problems as they see fit. Unfortunately far too many people look past local government and demand action from Washington, DC, and one size does not fit all.