It hinges upon whether the nomination of Rockefeller makes him Vice President-elect for purposes of 3 U.S.C. 19, or an officer nominated and confirmed by the Senate (not withstanding that the 25th Amendment calls for confirmation by both Houses).
If it is the former, then the confirmation process continues and if confirmed, Rockefeller takes office. Since it would only be a temporary stint as Acting President that would require him to leave Congress, then both Speaker Albert and PPT Eastland might decline to take office, leaving it to Treasury Secretary Simon (Secretary of State Kissinger being ineligible) to be Acting President.
If it is the latter then Rockefeller is not part of the line of succession, and Albert would take office as President for the remainder of the term and he could then nominate his own choice to be Vice President.
It's not explicit which should be the case, but the latter is both simpler and takes into consideration that when 3 USC 19 was enacted in 1948, there were no offices in the line of succession which required both Houses to confirm.
Wouldn't Albert take office as Acting President? If he wanted to continue being Acting President, it would be in his interests to never nominate a Vice President, right? Wouldn't a sitting Vice President then immediately assume the Presidency upon confirmation?
