Elizabeth Warren is gaining. She has breached 20 percent of the vote in recent national surveys and might hold a narrow lead in Iowa and New Hampshire. The prediction markets now consider her a clear favorite to win the nomination. It can be hard to see how her Democratic rivals will attack or stop her.

But the challenge facing Ms. Warren, if past primaries are any indication, isn’t those rivals. It is whether she will hit a wall: the rank and file of the Democratic primary electorate.

In primary after primary, the candidates of the party’s left-liberal activists have failed to win the more typical members of the Democratic Party. These voters don’t show up at rallies or post on political Twitter. They are more moderate. They are disproportionately nonwhite; Southern; and less likely to have graduated from college. But in the modern era, they have usually had the votes to decide the nomination. In August, t hey even had the votes to sway an Iowa straw poll to Joe Biden when other candidates attracted far bigger crowds at the same fai r.

To win the nomination, Ms. Warren will need to advance beyond her factional base to a broader coalition. Historically, many left-liberal candidates have found it easy to attract 20-plus percent in the polls and five-digit crowds on the stump. Howard Dean (2004) and Bernie Sanders (2016) had done so by this point in the election cycle. But such candidates have found it far harder to win.