When you "hold a mirror up" to someone, you show them their own characteristics. We usually do it when we want to show someone their own less desirable characteristics.

In this context, "holding a mirror up to" means reflecting, or examining the way business is conducted on Capitol Hill.

hold a mirror up to : reflect upon something. (to think, ponder, or meditate) i.e. nothing to do with reflecting upon the way we conduct the business on Capitol Hill today. e.g. to hold a mirror up to one's virtues and faults.