As New York’s state legislators huddle behind closed doors to select a temporary replacement for the disgraced former attorney general Eric T. Schneiderman, they will be choosing more than just a six-month placeholder for the state’s top legal job.

They may also be deciding the future of the outsize responsibility Mr. Schneiderman seemed to envision for the position — a responsibility he treated as not merely enforcing the state’s laws, but defying President Trump and safeguarding democratic ideals.

In the wake of Mr. Schneiderman’s stunning resignation Monday night after four women accused him in The New Yorker of physical abuse, whoever replaces him will immediately step into a high-profile, almost celebrity role. As a result, the race to replace him has taken on a significance, and drawn a level of attention, usually reserved more for general elections than for a half-year holdover position, the kind that might normally be bestowed quietly as a résumé ornament upon a longtime political loyalist.

Already on Tuesday, elected officials were discussing the symbolism of the role, suggesting that they would like to see a woman, perhaps a woman of color, hold the office for the first time.