Kyle Smith writes, “McConnell, I remind you, could simply dismiss any House impeachment measure. He need not bring it up for a vote. Or, alternatively, he could bring it up for a vote if he thought it would embarrass the Democratic party.” It looks like the current rules of the Senate require that it move to a trial as soon as the House, having impeached the president, appoints impeachment managers. A majority could change those rules, but Republicans would have to vote for the rules change — and thus on President Trump’s removal.
Maybe McConnell has some procedural trick up his sleeve, but this doesn’t seem to be on par with the Garland nomination in 2016. Then there was neither a constitutional obligation nor a Senate rule that required taking up the nomination. The Senate has no constitutional obligation to hold a trial on removal of the president simply because the House has voted to impeach, but it does appear to have an obligation to do so under its current rules.