In my delight at how the constitution's workings could result in Mitt Romney being elected president with Hillary Clinton as his vice president, I overlooked the change that the 12th amendment brought about. The 12th Amendment, adopted in Thomas Jefferson's term, was a response to the awkwardness that developed in 1796, when the electoral college put John Adams in first place and his bitter opponent Thomas Jefferson in second place, resulting in Adams becoming president and Jefferson being his ostracized vice president. The 12th amendment changed the procedure somewhat: instead of the House of Representatives selecting two of the top three finishers in the presidential race to be the president and vice president, the House selects the president (still with one vote per state) from among the top three in the presidential race, and the Senate selects the vice president from among the top two in the vice-presidential race. There's still an opportunity for constitutional mirth, but it's a little more complicated than I had described.
Let us continue to suppose that the Republican convention nominates Donald J. Trump and that he selects, say, Ted Cruz to be his running mate. (I think his best choice is Jeb Bush, but that's an analysis for another day.) The party's old guard puts together a third party and runs Mitt Romney, with (let's say) John Kasich as his running mate. The Democrats nominate Hillary Clinton, who picks Sherrod Brown, a second-term Senator from Ohio, as her running mate.
The election comes. The Clinton-Brown ticket receives the most electoral votes, but not the 270 required for election. Trump and Cruz finish second. Romney and Kasich finish third, winning a few states. The day after the November election, the candidates will know that the House will choose the president from among Secretary Clinton and Messrs. Trump and Romney, and the Senate will choose between Senators Cruz and Brown. Let's suppose that the Senate flips to the Democrats but the House remains Republican.
The nation will know that on January 3, the new House will select Mitt Romney as the president (I can't imagine the Republican majority lucidly voting for Mr. Trump), and the Senate will select Senator Brown as Mr. Romney's vice president. But wait -- the House and Senate don't select from the top finishers in the popular vote; they select from the top finishers in the electoral vote, and the electoral vote doesn't actually happen until mid-December. The important point is that the House and Senate cannot elect a dark horse candidate; they must choose from among the top three presidential candidates and the top two vice presidential candidates.
The Democratic leadership might have the interesting idea (I would in their place) to request the Democratic electors to swap their votes: to ask that in December when they meet in their state capitals to cast their votes, they should cast their Presidential votes for Senator Brown, and their Vice Presidential votes for Secretary Clinton. She will now be one of the top two finishers in the Veepstakes, and the Democratic Senate will elect her over Senator Cruz.
Ladies and gentlemen: I again give you Hillary Rodham Clinton, the first woman vice president of the United States.