As Mayor Bill de Blasio of New York turns toward his re-election fight next year, an issue that galvanized his first run — achieving significant police reform — is suddenly becoming a liability.

Caught in the gap between his soaring rhetoric as an outsider candidate and the realities of leading a city with a hair-trigger sensitivity to crime, Mr. de Blasio is disappointing many who once supported him, in a community he can ill afford to lose: the black voters who propelled him to office.

“All I know is, in all our circles, folks have conversations and there’s a buzz going around about the disappointment,” said Bertha Lewis, the former leader of Acorn who served on Mr. de Blasio’s transition team in 2014, but has become a vocal critic. “There’s a growing enthusiasm gap.”