I would be totally surprised if both Dems and Republicans aren't doing polls in seeing how people are feeling about this thing. If more people than not think that the trial needs to be done, delaying it will only harm the Democrats and potentially cost them the election. They will totally look obstructionists, for impeaching him, and then not allowing him to have a trial.
At the end of the day, rules are rules. The House decides in the articles of the impeachment (without Senate having a say there), and the Senate decides in the trial (without the House having a say there). Each chamber decides its own rules, however they want. When chambers are rules from different parties, there is not much that can be done.