As Letitia James, the New York City public advocate, considers a bid to replace the disgraced former attorney general, Eric T. Schneiderman, she faces an unexpected and thorny dilemma.

Ms. James, a Democrat, was a logical pick to secure the Working Families Party line ahead of the upcoming Democratic convention, since she won her very first race with that progressive party’s backing.

But logic and the cutthroat politics of New York do not always comport.

Ms. James has been telling allies and potential supporters that Gov. Andrew M. Cuomo’s operation is pushing her to reject the Working Families Party — or risk losing his support if she seeks the Democratic Party nomination, according to five people familiar with the matter, including three who spoke directly with Ms. James.

It is hardly a secret that Mr. Cuomo has been at war with the Working Families Party, which aims to pull Democrats to the left politically, ever since it endorsed Mr. Cuomo’s primary opponent, Cynthia Nixon, last month. His labor allies have already withdrawn support from the party.