The Senate doesn't have the authority under the Constitution to stop an impeachment trial. Their only role in the matter is to vote guilty or not guilty on the Articles of Impeachment after a trial. The person with the authority to dismiss the Articles without a trial is the Chief Justice of the Supreme Court who would be the presiding judge in an impeachment trial.
The Senate would have to act on a trial, but that could be done with relative dispatch. McConnell would be able to set either broad or narrow parameters on which evidence/witnesses is admissible. The fly in the ointment is maintaining 51 GOP senators to go along with how each item is dispensed. That’s no sure thing and how it plays out would affect the length of any trial. But I don’t see any way 67 senators vote to remove Trump from office. That’s a bridge too far.
I hear the Dems in the House plan an Articles of Impeachment vote around Thanksgiving, but I still believe that may be a smokescreen. There is simply no ROI for Dems to pursue this - but I speak as a rational person, so who knows what goes through their tyrannical minds?