While I was watching Mitt Romney make up fantasy positions in the foreign-policy debate, I had a fantasy of my own.

And given the electoral isthmus the two men are wrestling on, it doesn’t seem like such a wild one. There is growing buzz that the dead heat could slide into a deadlock.

If Romney does suspend voter disbelief enough to tie President Obama, with each getting 269 Electoral College votes, the Republican-controlled House would determine the president — and give it to Mitt. And the (presumably) Democrat-controlled Senate would determine the vice president — and give it to Joe Biden.

So the first election decided by Congress in more than a century would produce a Republican president handcuffed to a Democratic vice president.

I think we can count on Good Ol’ Joe to devote himself to tormenting President Mittens. When Romney begins his “I, Willard . . .” at the inauguration, Joe can howl like a banshee, “That’s a bunch of malarkey!”

When Biden sits behind Romney at his first State of the Union address, in that familiar tiered TV shot, the vice president can guffaw and roll his eyes and slap his knee and put his head in his hands and wave a sign behind Mitt’s slick head that reads, “Bunch of stuff.” I think we can count on Joe to ignore an enraged Tagg shaking his fist from the gallery.

A historic tie, which would spur demonstrations that would make the health care battle look like the Macy’s Thanksgiving Day Parade, seems a logical conclusion of the bitter partisan paralysis here and the bottom-feeding campaign, where hope has been chased out by lies on one side and character exaggeration on the other.

And why is the race so perilously close, given the dizzying fall of W. and the dizzying rise of Obama, a mere four years ago?

It is partly because of Obama’s endless odyssey of self-discovery, where he rattles around in his own head, trying to figure out who he is and why he’s stuck on a Denver debate stage, forced to justify himself in this clownish format against this shape-shifting chucklehead.

At the first debate, the president gave off such a feeling of ennui, he could have used a fainting couch. It suddenly made many voters who thought it only fair that Obama get another term, given the mountain of trouble W. had left behind, wonder if that second chance would be embraced with energy, imagination and zest.

And the race is vise-tight because Mitt’s a marvel. Never in modern memory has a presidential candidate so brazenly contorted himself, switching positions to suit the moment and pushing claims, like about Obama’s imaginary “apology tour,” that have been debunked.

But as Bill Clinton warned the Obama team last year, attacking Romney as a flip-flopper, as the president did Monday night in Boca Raton, can help Mitt with centrist voters who like the idea that he’s actually a sheep in Wolfowitz clothing.

Forgoing his Klingon rhetoric, Mitt played cling-on to Obama’s Spock, suddenly clutching onto the president’s positions on China, Iran, the Afghanistan deadline, drones and ousting Hosni Mubarak. Romney was running so far to the left of Obama that he never even mentioned the tangled White House response to the Benghazi consulate slaughter, which Republicans on the Hill have been working tirelessly to tee up for him.