In theory, an identity-based appeal is the easiest way to win over a big chunk of otherwise relatively conservative voters. You could imagine, for instance, a liberal Southern white male (say, a politically viable version of John Edwards) who could create an odd coalition uniting San Francisco and West Virginia, or maybe a liberal Hispanic Democrat who could do the same thing in the Southwest and therefore win a state like California. Ms. Warren has no obvious, identity-based appeal to any segment of the Democratic electorate. Against male candidates, perhaps gender could be such an advantage, but Ms. Warren, again, will not have that opening against Mrs. Clinton.

Her best option might be identity politics. One possibility is the blueprint used by Bill de Blasio. Even in liberal New York City, the progressive vote in a Democratic primary holds a clear advantage only in Manhattan and nearby precincts in Brooklyn. But Mr. de Blasio easily won the nomination and avoided a runoff, in no small part because he won black voters by a wide margin — despite facing a black candidate. He did that by taking an impassioned position against the Police Department’s so-called stop-and-frisk policy, which is unpopular in black communities.

I’m not sure whether the same hot-button issue exists to battle Mrs. Clinton. There is no obvious Clinton version of stop-and-frisk in national politics. Despite the #blacklivesmatter movement and renewed recognition of racial disparities in police conduct, there is not yet a policy agenda for a candidate like Ms. Warren that would mobilize likely voters.

The closest thing might be prison or sentencing reforms, though those issues have not seemed to inspire the same grass-roots energy as police misconduct. Just as important, Mrs. Clinton could embrace part or all of that agenda herself (if she did not, it would obviously be an opening). Even if I’m wrong about all of this, and if Ms. Warren could run as the candidate of, say, police reform, it’s hard to see how she could win the black vote by anything near the margin that Mr. Obama did.

Mrs. Clinton’s private email account as secretary of state; her ties to Wall Street; the foreign contributions to the Clinton Foundation; and the voter fatigue that may come with the Clintons do create an opening for a serious challenger. But it probably does not create an opening to defeat her.

Here’s the easiest way to think about this: I don’t think Ms. Warren would have been able to beat Mrs. Clinton in 2008. Mrs. Clinton’s margin of defeat against Mr. Obama was so small that she could have survived a weaker opponent. A weaker candidate, like Ms. Warren, wouldn’t have had the ability to contrast with her on the war in Iraq and couldn’t have appealed to black voters as well. Wall Street may be a big issue today, but it’s not Iraq. All of the reservations about the Clintons were around in 2008, even if the specific questions about emails or the Clinton Foundation are newer.

If Ms. Warren couldn’t have beaten Mrs. Clinton in 2008, it’s a stretch to argue she could do it today.