That criticism, both technical and philosophical, continued in an inevitable segment about Medicare for All with Ms. Warren facing criticism from both her left and right flanks. In previous debates, Ms. Warren avoided saying exactly how she would pay for the tens of trillions in new government spending the health care system she favors would entail. But she recently released both a financing plan and an implementation timeline in which she proposed putting off the push for a full-fledged single-payer system.

That segment opened with Pete Buttigieg, the mayor of South Bend, Ind., touting his own plan, which he calls Medicare for All Who Want It, as a way to avoid the “divisive” step of eliminating most private insurance and forcing most Americans onto a government health care plan. Mr. Biden, similarly, framed his opposition to Ms. Warren’s proposal by saying, “I trust the American people.” Once again, it was an attack not only on Ms. Warren’s plan, but on the political philosophy it represents.

From the other side of the debate, Senator Bernie Sanders of Vermont, whose Medicare for All bill Ms. Warren backs, implied that he didn’t trust Ms. Warren’s plan to hold off on Medicare for All until late in her first term. Now is the time, he said, practically pounding the podium. “In the first week of my administration, we will introduce Medicare for All.” The message was clear: Warrenism, which would wait until year three to fight for single-payer, was insufficiently devoted to the revolutionary cause.

These exchanges illustrate the Democratic Party’s growing uneasiness with Ms. Warren and her brand of fussy technocratic populism, which can come across as both too radical and too timidly wonky at the same time.

Throughout her campaign, Ms. Warren has attempted to occupy a middle ground between the party’s moderate wing and its progressive base. But her have-it-both-ways strategy may well have backfired. Despite Ms. Warren’s ascension to the primary’s top tier, the steadiness of Mr. Biden’s polling and the recent rise of Mr. Buttigieg in Iowa and New Hampshire — along with the dips in Ms. Warren’s own polling — suggest not only the limits of her strategy but the limitations of the underlying worldview itself.