I think that they are Constitutionally required to have some sort of quick return on a trial, even if they halfass it. Both sides of the aisle were pretty clear, during the last impeachment joke, that the Senate had a Constitutional duty to set aside everything else to conduct some sort of trial.
Of course, there is no set procedure for how they conduct that trial, but I don't believe tabling it is an option. They can do an immediate vote to dismiss the allegations, but they still have to do something.