Obama has every right and the constitutional authority to appoint a temporary person to sit on the court. Probably not to his political advantage to do so. More likely he sends someone up for confirmation. Someone that would normally be approved, with a bit of a fight, but doable. He does that and it's a political edge for the dems as the repubs stonewall. This will provide some steam for the democratic platform.
Of course this issue will also energize the republican base, as well it should. Elections have consequences. The senate race will now take on more importance. Repubs hold the senate and win the WH, we'll get a staunch conservative for the court. It's basically status quo. Dems win the WH, but not the senate, it's a hell of a fight. Dems win the WH and the senate, it's lefty heaven as the court takes a hard left turn.
Both sides will create their doomsday scenario and beat it to death on the campaign trail. Too bad we just can't pick someone qualified and move on. Whatever would we do without all the "end of days" debate between the kooks?