Of course they have no shame. Thus, no way to shame them. But, when the Senate trial starts, and witnesses are allowed to be questioned including the “whistleblower”, if they had any sense of shame they would be looking for a hole to get into. Oh well, their empty headed audience won’t have a clue.
There won't be any witnesses, despite what we are hearing.
To call witnesses gives legitimacy to this kangaroo court sham. Furthermore, any trial lawyer will tell you that calling a witness is always a very tricky thing. It can easily blow up in your face.
The Senate could introduce a motion to dismiss, but they would be accused of a "cover up." McConnell will most likely allow the House managers to prattle on, followed by a quick rebuttal from Trump's attorneys, followed by a quick floor vote from the Senators.
Q.E.D.