Senate Majority Leader Mitch McConnell is constitutionally bound to proceed with an impeachment trial should the House impeach—formally charge—Donald Trump. That's the conclusion his staff has come to after undertaking a legal assessment, according to The New York Times's Glenn Thrush.
It's also standard operating procedure in the very non-standard event of a House impeachment. Even McConnell has taken a fairly cautious approach, telling reporters in Kentucky last week that it is "too early to comment" on the obstruction allegations within the Mueller report. Mueller found substantive evidence of obstruction, but chose not to prosecute and passed that ball very clearly to the Congress. The remedy for Trump's obstruction, he concluded, lies with Congress. McConnell said he wanted to see the full, unredacted report before passing judgement on impeachment. That's his public side. He also said Trump had "every right to feel good" about the report and is telling colleagues he wants to move on and see no reason at all for the Senate to have investigations.
There's two things here that are important to note: McConnell knows he can't avoid his constitutional duty should the House impeach, and he knows that his public stance has to reflect that. He has to appear to the American people as cognizant of his obligations. In reality, what would McConnell do? We can't know until it happens.
But what is very clear is that as far as House Speaker Nancy Pelosi is concerned, the decision to move forward on impeachment is one, again, of constitutional obligation. Not what McConnell may or may not do. It's incumbent on the House has to make the case for impeachment. They have to hold the public hearings to lay bare everything Trump has done, the conspiring with Russia (yeah, it was in the report) and the subsequent obstruction to cover it up. That forces McConnell's hand. She can't wait for agreement with him and she can't use his reticence as an excuse.