I imagined a solution to that.
I imagined Bush and Gore having to move into the White House at the same time, and be Co-Presidents at the same time, and have to deal with each other along with dealing with the million-plus decisions a President makes every day. Personality clashes! Pets' personality clashes! An argument over whether they'd split the Oval Office either by time or by a dotted line down the middle! Thumb wars over who gets to sign each law into law, or who gets to use the veto pen!
Hey, sitcoms don't have to make sense.
Maybe that's what Trey Parker and Matt Stone could have done. They wanted to do a wacky sitcom about the President, as a way to mock bad sitcoms, and because Bush won they went with That's My Bush! with Timothy Bottoms, and had Gore become President Gore they would have gone with some the title Everybody Loves Al and some other actor but still do the let's-mock-bad-sticoms shtick, but this...this could've been even more meta.
Of course, none of this happened or will happen. But hey, who knows: maybe our elected government officials would work together better if they really did have to live together. (Dorms for the Senate and the House!)