According to Wikipedia, the shadow government is a family of conspiracy theories ranging from government control by aliens to global elitists and supranational organizations that seek to conquer the world. Casting aside conspiracy theories, there really is an invisible government of sorts, but it is neither organized, secret or invisible. It operates in plain view of everyone and the power it wields far outweighs that of the electorate.
Moneyed interests now dominate the American political system to the extent that politicians now have two masters: their constituents who vote for them and their patrons who pay for their election campaigns. When the interests of constituents and patrons conflict, the interests of the patrons takes first priority because politicians know that to do otherwise will cost them the money needed for their election campaigns.
It is due to the influence of the moneyed interest groups that politicians vote for tax cuts for the rich and funding for big profit programs like weapons for war and security, and vote against adequate funding for small profit programs like health care, education, infrastructure, social security and the safety net for the indigent. This is true for both the dominant parties, so that one must question whether they are two parties or just one which is subservient to the moneyed interests that fund them.
When it comes to ruling America, the perverted version of the “golden rule” has it right. “He who has the gold, rules.” Therein lies the real shadow government.