In sum, the advice-and-consent clause doesn't put any duties on the Senate at all. It only provides that the President can nominate, and if the Senate gives its advice and consent, the President can appoint.
While it seems quite possible that Congress will be willing to pass a law exempting Mattis from the requirement, a question is whether the requirement is constitutional.
Earlier this year, the Harvard Journal of Law and Public Policy published my article showing that the Constitution’s Recess Appointments Clause limits presidential vacancy appointments far more than President Obama (and most prior Presidents) have claimed. I posted earlier on the same subject here. The issue is before the Supreme Court right now. The Recess Appointments Clause states in part…