When committee members vote on Tillerson, they’ll be voting on whether to issue a positive or negative report to the full Senate. If the lack of majority support on the committee leads to a negative report, McConnell could still use his authority as majority leader to rescue Trump’s nominee.

“It could go onto the executive calendar with a negative report from the Foreign Relations Committee in Tillerson’s case, and the report from the committee would be, hey, we don’t think this is the guy that you should vote for,” the senior GOP aide said. “And Mitch McConnell could still bring that nominee before the Senate with the recommendation [from the committee] that it be voted down, effectively.”

McConnell wouldn’t bring it to the floor unless he had the votes to win. That would mean that Republican defections would have to be kept to a minimum, or some Senate Democrats — perhaps the ones running red states, or who have talked to Trump about their own potential as cabinet picks — would have to break ranks and salvage the nomination.