Chemerinsky’s thesis about the purpose of the U.S. Supreme Court
As noted, Erwin Chemerinsky is a very prominent constitutional law scholar.
But, let’s focus on Chemerinsky’s thesis about the purpose of the U.S. Supreme Court. In your post, you stated that Chemerinsky argued that the U.S. Supreme Court served the following purpose: “to enforce the Constitution.” You also stated that Chemerinsky and also “explains that the purpose of the Constitution is to place a limit on what the Government can do, as well as to protect the minority from the democratic majority.”
How does Chemerinsky arrive at these purposes? And, what do these stated purposes tell us about Chemerinsky’s political ideology and/or judicial philosophy?… Professor James Barney
Chemerinski arrives at these purposes from his analysis of what the Constitution does.
He states that the Constitution empowers and limits the government’s exercise of authority over the people and through the Bill of Rights, grants rights to the people. 
He states that to prevent tyranny of the majority and to protect the rights of the majority from oppression, the Constitution was deliberately crafted to be difficult to change. 
He believes that purpose of the Supreme Court is to enforce the Constitution against the will of the powerful democratic majority.
He reasoned that in a democracy, the majority is easily protected.
However, the political, social and economic minorities that need the most protection will find themselves at the mercy of a democratic majority that often either cannot afford protection or does not wish to defend itself.
He supports his position by citing that having the Justices serve a lifetime appointment is to free the Justices to be able to provide this protection to minorities without threat of retribution from the majority. 
Because of this, I can sense that his political and judicial philosophy is a reflection of the need to keep the powerful majority in check to avoid tyranny.
 Erwin Chemerinsky, The case against the Supreme Court pp. 6-7 (Kindle Ed. 2015).
 Erwin Chemerinsky, The case against the Supreme Court p. 8 (Kindle Ed. 2015).
 Chemerinsky, Erwin. The Case Against the Supreme Court pp. 9-10 (Kindle Ed. 2015).