It would be hard to overstate the importance of who will be the next justice in the evenly-divided U.S. Supreme Court. President Obama’s nominee could have a profound impact on both the politics of 2016 and the shape of social and economic progress well into the future.
In his post, “The Simply Breathtaking Consequences Of Justice Scalia’s Death” at ThinkProgress, Ian Milhiser notes that the Supreme Court’s docket includes major cases addressing immigration, abortion, birth control, unions, redistricting, affirmative action and the environment. That’s just the short run. In the-too-distant future, the Court will render decisions that could reverse the Citizens United decision, support gun control and strengthen consumer protection, to name a few possibilities.
At this writing it seems highly unlikely that the President’s nominee will be confirmed by the present U.S. Senate. As SCOTUSBlog publisher Tom Goldstein recently put it,

The bottom line is that President Obama’s nominee is not getting confirmed before the election. Maybe there will be a permanent filibuster. Maybe Republicans will nominally allow the filibuster to be “broken,” then proceed to reject the nominee on the merits. (That course is suggested by the announcement by Senator Chuck Grassley, chairman of the Senate Judiciary Committee, that he would await a nomination before deciding whether to hold hearings.) Maybe a couple of Republicans who have specific concerns in purple states will even vote for the nominee. But the entire process will be crafted to ensure that the nominee is not confirmed.

Goldstein is likely correct. But there remains a possibility, that once the President submits his nominee, purple state Republican senators will have second thoughts about serving as collateral damage in a Democratic landslide resulting from Trump being nominated.
Up till now, Republicans have gotten a fairly easy ride on their policy of knee-jerk obstruction of all things Obama and Democratic. The coming SCOTUS battle will up the stakes considerably, perhaps to the point where even low-information voters get it that GOP really does stand for “Gridlock, Obstruction and Paralysis.” Not a brand that offers much hope for the future.
Further, there are some cracks in the GOP’s obstructionist wall. As Emily Atkin notes at ThinkProgress:

[Ron} Johnson is the latest Republican senator to suggest that his colleagues should at least consider an Obama-nominated replacement for Scalia, breaking with the hard-line position of McConnell. On Tuesday morning, Sen. Thom Tillis (R-NC) warned that his colleagues should not automatically block any nominee, saying the party risks “[falling] into the trap of being obstructionists.” Sen. Chuck Grassley (R-IA), who chairs the Senate Judiciary Committee, has not ruled out holding committee hearings on Obama’s pick. And Sen. Rand Paul (R-KY) has said he would “look at” a nominee put forward by Obama…While most Senate Republicans have sided with McConnell’s decision not to hold any hearings, not everyone has been outwardly supportive. Sen. Susan Collins (R-ME), for example, recently said that all Supreme Court nominees deserve “in-depth consideration given the importance of their constitutional role and their lifetime tenure.”

It has been argued that the President could make a recess appointment, who could serve without confirmation until the next congress convenes. Veteran High Court reporter Lyle Denniston observes at SCOTUSBlog,

…Less than two years ago, the Supreme Court severely narrowed the flexibility of such temporary appointment power, and strengthened the Senate’s capacity to frustrate such a presidential maneuver.
It is true that one of the Justices regarded as a giant on the Court’s history, William J. Brennan, Jr., actually began his lengthy career with just such a short-term appointment. The chances of that happening again today seem to have diminished markedly.
..Could President Obama make a nominee during that recess? Only if the Senate is taking a recess lasting longer than three days, and does not come in from time to time during that recess to take some minimal legislative action. Both of those circumstances would be entirely within the Senate’s authority.
In that circumstance, a recess appointment to the Court would not be within the terms of the Constitution, as spelled out in Article II.

In that context, a recess appointment could be more than a little problematic, with lots of distracting side-battles. With that in mind, the President still has another way to get his appointee confirmed. It would just take longer. He could appoint a highly-qualified candidate, who gains the wholehearted endorsement of both Democratic presidential candidates. The SCOTUS nominee might be blocked from confirmation in this session, but could have added leverage in the next session, with a new president and Senate.
Some of the potential candidates who have been suggested:
Judge Jane Kelly, age 41 – Tom Goldstein notes, “Eighth Circuit Judge Jane Kelly, who was confirmed by a vote of ninety-six to zero, with the strong support of Senator Grassley. So she will almost certainly be a serious candidate.” But she has served on that court for 2 years.
Attorney-General Loretta Lynch, age 55 – “…Her confirmation vote in the Senate was close (because of Republican votes), so the administration could not make the point that she had been uniformly supported in the past…” But the Republicans could delay her by asking for all sorts of documents pertaining to her tenure as Attorney General, another problematic distraction.
Judge Ketanji Brown Jackson of the U.S. District Court for the District of Columbia Age 45 — “She was confirmed by without any Republican opposition in the Senate not once, but twice,” notes Goldstein, who thinks she would have a good chance of ultimately being confirmed. She has impressive academic credentials and clerked with Supreme Court Justice Stephen Breyer. However, adds Goldstein, “Judge Brown Jackson’s credentials would be even stronger if she were on the court of appeals rather than the district court and if she had been a judge for longer than three years.”
Paul J. Watford – Age 48, is a highly respected Ninth Circuit judge who was confirmed by a 61-34 vote. But he has only served for 3 years. He clerked with Justice Ginsburg and was supported by conservative legal scholars, as well as progressives.
D.C. Circuit Judge Sri Srinivasan, age 47 — Described by Goldstein as “almost a lock to get a Supreme Court appointment in a Democratic administration, because he is so very widely respected and admired. If it were possible to select a consensus candidate whom Republicans would actually confirm, he would surely be it…He also has the great advantage of having been unanimously confirmed.” However, notes Goldstein, he “generates very little political advantage” in the context of 2016 electoral politics.
Judge Merrick Garland, DC Circuit Court, age 63 – “He’s considered a judicial moderate,” notes Michael Tomasky, “and back in 2010, Republican Sen. Orrin Hatch, always a big player in Supreme Court deliberations, said that Garland would be confirmed for the high court on a bipartisan basis, “No question.”
Sen. Elizabeth Warren, age 66 – Popular and respected, it’s easy to picture her as a great Supreme Court justice. But her confirmation would mean that Democrats could lose a Senate seat, since Massachusetts has a Republican governor who would appoint her successor. Frequently-cited as a possible presidential candidate in the future, she more likely has higher aspirations. This looks like a non-starter.
These are just some of the names that have been mentioned as possible short-list nominees. But no one should be surprised if the unique politics of 2016 produces a wild card nominee. The race of the eventual nominee could be a factor in how voters perceive the way they were treated by the Republicans. Perceived ideology will surely influence some confirmation votes.
Expect some ferocious political chess surrounding the Supreme Court vacancy over the coming weeks. Regardless of who is eventually nominated by President Obama, however, Democrats are in very good shape for restoring a progressive majority to the Supreme Court.