Order of House/Senate votes in event of no EC majority

[J. J.]

I would not see a constitutional violation.  The only example I can think of is Kissinger serving as both National Security Adviser and Secretary of State at the same time, which is close.

One possible scenario:  Romney gets involved some scandal.  The GOP wins big in the Senate.  Everybody is happy with Ryan as president, but the GOP in the Senate want a Republican VP.  Their only constitutional choice is Ryan.

Ryan accepts the VP position, holds i for a day, and resigns.  Ryan can appoint a VP, subject to confirmation.

Just to complicate matters, there would be no constitution problem with Ryan serving as Speaker while president.

[J. J.]

Nor would there be a need for Ryan to hold the office of Vice President for even one day.  Federal law allows for a President-elect or a Vice President-elect to refuse the office in which case it is treated as a vacancy.

That would trigger the Congressional election of the VP.