If all else fails, can the below excerpt give us any hope?
Objections to State Electoral Vote Returns. Objections may be offered to both individual electoral votes and state returns as a whole. Objections must be filed in writing, and be signed by one Senator and one Representative.
If an objection is received, and determined to be valid, then the electoral vote count session is recessed. The Senate returns immediately to its chamber, and the two houses of Congress consider the objections separately.
By law, these sessions cannot last more than two hours, and no member of either house may speak for more than five minutes. At the end of this period, the houses vote separately to agree or disagree with the objection. The Senate then returns to the House chamber, and the
joint session reconvenes. The decisions of the two houses are announced. If both houses agree to the objection, then the electoral vote or votes in question are not counted. Otherwise, the vote or votes stand as submitted, and are counted as such.
One observation: Only the Senate-President (Cheney) is constitutionally authorized to open the EC letters during the joint session.
If the letters are opened before there are disqualification objections: Pelosi and Reid could orchestrate a sham vote to first make Obama the President-Elect, then allow Biden to immediately promote to President-Elect after the DQ, by-passing McCain.
If Cheney forces a SCOTUS DQ decision by refusing to open the letters, there’s no way for a sham vote to take place to promote Biden and so McCain is next in line (unless one Elector puts Hillary’s name in the top three list, then it could be interesting in the House vote between McCain and Hillary: each State gets one vote).
Summary: The hardball play is Cheney refuses to open the EC letters until the DQ issue plays out, which avoids a sham vote which could allow Biden to promote to President-Elect past McCain. The only way for Pelosi and Reid to block this play (somewhat crazy but we’re living in interesting time) is to impeach Cheney on the spot: not likely if he has the goods in hand.