Will the civil case have teeth?
To hold Holder in Contempt and then let him continue ignoring congress, will make the Executive branch feel like Congress is inconsequential. That's not good.
Remember, the Supreme Court only restricts the Executive ~ each House has total power that may be exercised at will. If Boehner won't do it he could be reminded of what happened to Georges Jacques Danton. Someone there will do the job that can be done to drive back the Executive's jack booted thugs.