I think you have that backwards TheDrake. This is him attempting to punt the responsibility so he doesn't have to be the face of the investigation and bear the consequences with his own base this time.
That... Makes sense.
The Republican's in the Congress can "do something" by appointing an independent special prosecutor, one the Democrats can't really protest against going into the investigation. Let the Prosecutor do his thing, essentially force the democrats to STFU about it in the interim, and go about their business. If the Prosecutory doesn't find anything particularly damning towards Trump, they can wash their hands of it and call the Democrats names for "having required it." They also escape suffering any significant political damage as the "investigation" plays out in congressional hearings.
If the prosecutor does find damning evidence towards Trump and/or Pence, then they have a fait accompli, and they can start the process of booting him/them from office, and still wash their hands of the whole mess, and avoid many claims from the Democrats that they were trying to cover for Trump.
As I've been saying for a while, I have few doubts as to the willingness and ability of the Republicans in Congress to cover their own ass in regards to Trump. This would be a penultimate form of their doing so. In that context, I actually wouldn't be surprised if they do so this time.
