In four of the original six states mentioned for objections then no, senators did not sign on. But for Arizona and Pennsylvania there were Senators who joined House members in objecting, and there were debates and votes on the objections as a result. In fact they were in the process of adjourning to separate chambers for the Arizona debate when the Capitol was breached.
Exactly. So when VP Pence in his capacity as the President of the Senate was presented with the objection not a SINGLE US Senator took the time and effort to sign the stupid motion. Hmmmmm