I do wish some of these people would ACTUALLY READ the Constitution.
The formal act of Impeachment (similar to an indictment) is brought by the U.S. House of Representative, so neither Senate Majority Leader McConnell nor the Senate have anything to do with that. If and when the House of Representatives votes to impeach the current President (which they haven’t done so far) the Senate will conduct a trial, with representatives from the House acting as prosecutor, the Chief Justice acting as the presiding judge, and the members of the Senate acting as a jury.
In any organization parliamentary procedure (with Robert’s Rules of Order generally used) requires that a quorum be present before business can be conducted. The “Standing Rules of the United States Senate” (the Senate has the authority to establish these rules from Article One, Section 5 of the constitution), requires that a majority of the senators be on the Senate floor for a quorum to be present. If the Senate is sitting in session to hear an impeachment brought by the House the constitution requires that two-thirds of the senators present must vote for conviction.
So, Mitch McConnell can’t (either himself or as part of a group of senators) impeach the President, that can ONLY BE DONE by the House of Representatives. If the inaccurate story was attempting to imply that Mitch McConnell might try to remove the President (if and only if the House has actually impeached him, which they haven’t done yet) by Senate trial “during the Christmas vacation when almost all Senators will be on vacation
”, well that won’t work either. A majority of all elected senators would have to be on the Senate floor for a quorum to be present, and two-thirds of those would have to vote for conviction.
For everyone's reference: The Constitution of the United States