Update: As our own James Hohmann reports, "Elizabeth Warren and Hillary Clinton will meet privately Friday morning, according to two knowledgeable Democrats," and their meeting "will fuel speculation about her prospects as a potential vice presidential pick."

Up until Thursday evening, Elizabeth Warren was the only female Democratic senator who hadn't endorsed Hillary Clinton. In fact, she was one of the last high-profile members of the Democratic Party to endorse her.

Yet, more so than any other Democratic senator, there is buzz that Clinton will or should pick Warren as her vice presidential running mate. Given her holdout on coming on-board Team Clinton, it's worth asking: Does Warren have a chance at the job?

Warren told Rachel Maddow on MSBNC on Thursday she's not being vetted for the job and she's happy with her current one. But despite what she says, it seems like Warren might be interested. We at The Washington Post put her on a short list among 27 candidates, and Reuters reports that people close to her say she's considering the pros and cons of being Clinton's veep. Harry Reid reportedly wants her to be the pick. And she gave a closely watched, fiery speech Thursday for the sole purpose of knocking Donald Trump down a peg or two.

In fact, almost out of nowhere, Warren has gone from watching the campaign on the sidelines to becoming one of Trump's loudest critics — especially on his home turf, Twitter.

In a lot of ways she makes sense as the pick. But did Clinton's most conspicuous holdout this primary campaign play her cards right to get it?

We can see both sides. On one hand, she played the primary brilliantly for promoting her brand of liberal politics and drawing the debate to the left. But that's not the same as saying she set herself up to be a running mate, and we could easily see how her unusual approach could backfire with Clinton.

Let's run through the arguments.

Yep. By staying out of it, she kept herself in it.

"Sen. Elizabeth Warren (D-Mass.) is playing the long game to get exactly what she wants out of presidential politics — specifically, to make economic populism go mainstream. And so far, it's working out pretty great."

That's what we wrote back in December for a piece headlined: How Elizabeth Warren is winning the Democratic primary. I argued that by keeping her distance, Warren ensured her presence — and potentially game-changing endorsement — was felt. It appeared to play a role in helping pull Clinton to the left on economic policy.

Hillary Rodham Clinton officially launched her presidential campaign on Sunday. The announcement began with a video and a tweet. (YouTube/Hillary Clinton)

Now that the primary is just about over, Warren's silence may have an added benefit of making her voice louder.

When she does flex her political muscle for Clinton — like going on a Twitter tear against Trump or giving a speech calling him a "nasty, loud, thin-skinned fraud" (an excerpt from Thursday's speech) — it makes the kind of news Democrats want to see: Donald Trump + colorful insult.

Warren's attacks are buzzy in part because they are rare and she was not an official Clinton surrogate. When she speaks, it resonates. And that's something the Clinton campaign arguably needs when they're going up against a guy who can single-handedly dominate a day's news cycle with one tweet.

What's more, by not endorsing Clinton early on, Warren likely maintained her goodwill with Bernie Sanders backers who might otherwise have dismissed her. Which means that if Clinton is looking for Sanders-esque running mate, Warren certainly looks the part.

"What he did was powerfully important," Warren told Maddow on Thursday. "He ran a campaign from the heart."

No. Why would Clinton reward Warren for not getting on-board — and arguably helping Sanders?

Fact: The Clinton camp is all about loyalty — perhaps to a fault, some would say.

"Lawyers! Aides! Advisers! No presidential candidate has ever been as defended as Hillary Clinton," claimed Sarah Ellison in Vanity Fair in November, arguing that such a team could be her downfall.

Clinton surrounds herself with intensely loyal aides because the candidate herself values loyalty. It's something the Clintons are known for — along with punishing those who run afoul of them. (They even reportedly have assembled a hit list, according to a book by Jonathan Allen and Amie Parnes.)

If Clinton has hard feelings about Warren's non-endorsement, of course, she's kept it to herself.

But given how she's put loyalty front and center over the years, it stands to reason that Clinton would want it from her No. 2 as well. Warren's lack of an endorsement during most of the primary could be construed a lot of ways, but not as something she did out of loyalty to Clinton. And it's not a stretch to think that an earlier Warren endorsement might have foreclosed some of the momentum Sanders gained among liberal voters who also like Warren a lot.

That's a big strike for Warren's veep chances, especially since "when picking a vice presidential nominee, the single most important factor is chemistry," The Fix's Chris Cillizza pointed out in April, as he argued that Clinton wouldn't pick Warren.

The wildcard: Politics

Bernie Sanders supporters are still on the fence about backing Hillary Clinton in the general election. (Alice Li/The Washington Post)

Another fact: The Democratic presidential nomination went on longer than most expected and exacerbated divisions between the party's progressive and central factions.

As Sanders makes his gradual exit from the campaign (he indicated as much after a meeting with Obama on Thursday), party leaders are carefully watching to see how wounded their party is post-primary. If things are bad, there's a solid case to be made that Warren, the liberal hero to many Sanders backers, is the best salve to help heal those wounds.

It's hard to say whether that's actually the case. While Clinton was giving her history-making speech Tuesday, some Sanders supporters booed her. Polls also suggested that Sanders could win California in one final, defiant swipe at the establishment.

But Clinton won California by 13 points. And as Cillizza pointed out recently, a March Post-ABC national poll found that 77 percent of liberal Democrats said they would be satisfied with Clinton as their party's nominee. History suggests that even disenchanted Sanders supporters will come around — just like Clinton backers did for Barack Obama in 2008.

A complex mixture of politics, personality and personal choices will probably factor into whether Warren will eventually end up as Clinton's vice presidential pick. Given all that, it's tough to say whether Warren's unusual approach to this primary helped or hurt her chances for the job.