People aren't looking very far ahead. Immediately all the GOP leaders said that they won't confirm a nomination, and many have asked Obama not to make a nomination. On the other hand, Obama immediately said that he will make a nomination. So, that's likely to be the first public thing to happen.
Obama will likely pick somebody with impeccable credentials, but more importantly, a toughness to survive 11 months of vitriolic attacks -- because he's going to insist that the nominee maintain his or her determination to be confirmed. If he nominates somebody who pulls out after a few months, that would be devastating to Obama and the Democrats. And while that might limit the number of nominees to 10% of what they would be in normal (or, perhaps, historic) times, Obama will find somebody. It will likely be somebody who isn't strongly politically polarized.
And the GOP will immediately insist that they won't confirm him or her. Little question about that. That's when it gets interesting.
Obama will likely use the fact that the GOP Senators are blocking a reasonable candidate to attack them, and likely attack the ones who are at most risk to lose their elections this year. If Obama can make these senators look more like jerks -- and I think he probably can -- then things may change.
I think that the most politcally reasonable thing for the GOP to do would be to vote on the nominee, and just vote him or her down. Obama can probably nominate three or four people during the next eight months, the GOP taking a few months to evaluate each one would be typical and easily defensible.
I don't like it, but that's what I think will happen.