Addressing comments:
Yes, he is sort of making a res judicata (or even a double jeopardy) argument, but his lawyers don't seem to know that.
The words "res judicata" or even "double jeopardy" don't appear at all.
For a definition of res judicata: https://www.law.cornell.edu/wex/res_judicata
I think it fails for the same reason.
If you can be convicted in the Senate and then tried again in a criminal court, it cannot be said that the conviction ends the matter.
Right?
7/