How do government and the private sector intersect? How should they?

Wow, what a question!  First, what is the private sector?  According to businessdictionary.com, the private sector is defined as, "Part of national economy made up of, and resources owned by, private enterprises. It includes the personal sector (households) and corporate sector (firms), and is responsible for allocating most of the resources within an economy"(businessdictionary.com, 2011).  Based on this definition, I would say that they are very intersected.  The economy generally is self maintaining as a whole, but since we have had the sock market dive, the government has become very hands on when it comes to the economy.  In the book, The Politics of Power, the authors wrote a chapter entitled, "The American State and Corporate Capitalism, in this chapter they write, "Capitalism is often described as a system in which production for private profits is organized and coordinated through markets that are free of political direction.  But the free market has always been a fiction.  Markets cannot exist without a government to maintain order, enforce contracts, create currency, and provide a host of other public goods.  Markets require a protective, facilitating political order in order to function"(Katznelson, Kesselman, Draper, 51).  I think that this quote clearly explains that the private sector and government have and are still very intersected.  The two almost go hand in hand it seems.  It seems that the government really became intersected after the Great Depression and the New Deal with President Roosevelt.   In the book that was mentioned above, the authors write, "FDR was not hostile to capitalism but believed that greater management by the federal government was required to save it"(Katznelson, Kesselman, Draper, 59).  He became more hands on with the economy.  After the Depression, the American economy adopted Keynesianism.  The book states that, "For the next four decades, from the 1930's to the 1970's, both Democratic and Republican administrations followed Keynesian prescriptions of economic management"(Katznelson, Kesselman, Draper, 61).  The U.S. continues to use this principal still today, just more "conservative form". 
I think that the government should be intersected with the private sector to some extent.  I do not feel that government officials should have their hand in every cookie jar so to speak, but some government intersection is appropriate.  I do not believe we should have bailed out the corporations and banks that we did to the degree that we did and that if the government continues to do so and continues to be so hands on and overspending, we as Americans and the generations to come are in big trouble.  Even as the book, mentioned above, states in the "Conclusion" portion of the chapter, "...economic inequalities and difficulties created by the model of extreme market capitalism are generating heavy costs for current and future generations of Americans",( Katznelson,Kesselman, Draper, 61).