The process began Saturday night with conference calls among the president's legal team, followed by meetings Sunday to begin drawing up a list of possible names, according to two people who have been involved in the past two Obama Supreme Court nominations and remain close to the administration.
The White House already has a small list of people for whom deep background research was done when they were finalists for the last two openings on the court or other top jobs, like attorney general.
Even though he is on the West Coast for a summit with Southeast Asian leaders, Obama has been in touch with his senior team to plot his Supreme Court nomination process, and White House officials have communicated with Republicans and Democrats on Capitol Hill, the White House said Monday.
But while the White House officials have done extensive planning for possibly having to fill a third Supreme Court seat, those plans envisioned candidates to fill the seat of a retiring liberal justice, such as Ruth Bader Ginsburg.
"This is totally different because there haven't been a lot of preparations for filling one of the conservative seats," one former Obama administration official said.
The White House Counsel's office manages the process, with teams of lawyers and aides working on separate tasks including dossiers of general research on each potential candidate, vetting information and more specific legal research. The White House communications team looks at what specific public outreach strategies would be pursued for each candidate.
In the first few days of the process there's a broad list of names, but that quickly gets reduced to a smaller list of about eight names. By the end of the week, you can expect the White House team to focus on three or four candidates and prepare lengthy research documents on all, one official said.
Top officials then meet with the President to discuss the possible candidates and get his input on the final candidates. He would plan to meet with all the finalists, likely up to three.
Different nomination strategies
Administration officials will likely hash out strategy over the next few days. Should Obama nominate someone who is one of the Democrats' rising stars, and take the chance that they'll be damaged in the fight over the next few months?
People who have been involved in the process with Obama's last two high court nominations say the president takes the responsibility very seriously and would want to send his best pick, instead of gaming out the political process by sending a "sacrificial lamb" who they know won't survive the process.
Senate Minority Leader Harry Reid and several other Democrats, for instance, want Obama to pick someone to pressure Senate Republicans -- someone who they would ordinarily support but are only opposing now because it's an election year. This, they believe, would allow them to paint Republicans as intransigent and well outside the mainstream, undermining the Senate GOP's election-year argument that they are committed to governing in a bipartisan manner.
Speaking in Rancho Mirage, California, White House spokesman Eric Schultz said the Senate's "duties are ironclad" when it comes to voting on presidential nominees.
Schultz said that "doesn't include exceptions for election years." He cited past examples of instances in which he said "Republicans have come out with a lot of bluster."
Here's a look at the two basic paths Obama could take:
Sacrificial lamb option
If Obama determines that Senate Republicans will block his nominee -- no matter how moderate -- there's a chance he uses the moment instead to galvanize Democratic voters in a presidential election year.
By selecting a candidate with strong liberal leanings -- who is subsequently barred from receiving a vote by the Republican-led Senate -- Obama could fire up the base that elected him president -- perhaps motivating more of them to head to the polls in November.
"It's possible that from President Obama's perspective, this would be an opportunity to highlight how broken the judicial confirmation process has become," said Stephen Vladeck, a CNN contributor and law professor at American University.
One possible candidate under this approach would be Judge Cornelia Pillard from the U.S. Court of Appeals for the District of Columbia Circuit.
Pillard was a controversial nominee appointed after the Democratic majority enforced a rule change to expedite consideration of appointments -- the so-called nuclear option.
But finding a candidate willing to undergo the scrutiny unfazed would be a challenge for Obama's team, especially if that person is essentially risking any hope of getting nominated in the future.
In the past, Obama has advocated justices who blend legal smarts with personal empathy, a combination he cited during the selection processes for both Sonia Sotomayor and Elena Kagan.
The other option is to go with someone who has already gone through the confirmation process without controversy.
"I suspect he is going to choose from that pool of judges who have already been confirmed by the Senate -- some of them unanimously -- to make the case that they were perfectly fine the last time you guys examined them," David Axelrod, a CNN contributor and former top adviser to Obama, said on CNN Monday.
That line of thinking has been echoed by other top Democrats, who regard a recently confirmed judge, or a member of Obama's Cabinet who gained approval from GOP lawmakers, as having the best chance of getting through a Republican Senate.
That path would include Judge Sri Srinivasan, 48, of the D.C. Circuit. He was confirmed by 97-0 in May 2013. At that hearing, he was praised by Sen. Ted Cruz, now a Republican presidential candidate who is insisting that Obama hold off and let his successor choose a nominee.
Judge Jane Kelly, of the 8th U.S. Circuit Court of Appeals, is another contender -- she has Iowa connections and might appeal to Senate Judiciary Chairman Chuck Grassley. Another would be Judge Paul Watford, an African American who sits on the on the 9th U.S. Circuit Court of Appeals.
But even a person who's gained approval from Republicans in the past isn't guaranteed to glide through as a Supreme Court nominee.
"There's a different criteria, obviously. It's a heightened level of scrutiny," said Sen. Marco Rubio, a Florida Republican who's currently running for his party's presidential nomination. "Appellate courts are important, but the Supreme Court is the ultimate appellate court. So there's a whole new level of scrutiny and hearings and testimony."