Depending on what they find, she could be put in the same position that Kitzhaber was and forced to resign.   Of course Clintons ambition knows few bounds, so resigning would be pretty uncharacteristic.     

http://www.crf-usa.org/impeachment/high-crimes-and-misdemeanors.html

one view: 
“an impeachable offense is whatever a majority of the House of Representatives considers it to be at a given moment in history.”

another: 

'The framers of the Constitution did not give Congress absolute power to remove judges and executive officials. It wanted Congress to use its impeachment power only in extreme circumstances, when an official had committed “treason, bribery, or other high crimes and misdemeanors.” The separation of powers depends on Congress limiting impeachments to these cases."

Interesting reading.