To what extent has the rise in the influence of the members of the executive office affected our system of checks & balances?

I would argue that the rising influence of the members of
the Executive Office of the President has to some extent undercut the checks and
balances that were written into our system.

The reason for
this is that the EOP is not really subject to any kind of Congressional oversight.  You
can argue that the Framers intended for the executive branch to be run largely by the
members of the Cabinet.  These people would be approved by the Senate and that would
provide some amount of a check on the executive
branch.

With the rise of the EOP, you have much more policy
being made and carried out by people who are not subject to being approved by Congress. 
This diminishes Congress's ability to check the power of the
executive.