Part of Mr. Sanders’s resilience against centrist attacks stems from his grass-roots movement of small donors, organizers and vocal supporters. If party leaders openly assail him, they risk alienating Sanders loyalists, only 53 percent of whom say they will certainly support the Democratic nominee if it isn’t him. The problems at the Iowa caucus have instilled even more rancor and suspicion regarding Democratic institutions among his base. Establishment attacks on Sanders — especially if effective — could result in Mr. Sanders’ base simply staying home in the general election.

Yet if Mr. Sanders’s rise continues unimpeded, the party may risk demoralizing fiscally conservative Democrats, though those voters may be more likely to support a Democrat in the general election no matter what than Mr. Sanders’s passionate backers.

If they attack Mr. Sanders, “they’re going to get a massive backlash, but if they don’t, then they’re going to lose the center of the party,” Jefferson Cowie, a historian of American class politics at Vanderbilt University, told me recently. “It’s a very volatile moment, I think, in the party’s history.”