On the surface, these are rocky days for Mayor Bill de Blasio, whose infant tenure has endured impasse in Albany, speeding police escorts, and poll numbers that have rapidly diminished.

But in fits and starts, Mr. de Blasio has steadily found ways to impose his uncompromising liberalism onto New York, exploiting the powers of his office to further an agenda that allies say is far more consequential than day-to-day squabbles and scandals.

Stymied by Gov. Andrew M. Cuomo and state lawmakers on his tax-the-rich plan, Mr. de Blasio used a compliant City Council to enact a bill expanding the ability of workers to take paid days off when they or a family member falls ill. He signed the bill into law on Thursday with the flick of a commemorative pen — no approval from Albany required.

Keenly aware of his leverage over the city’s real estate industry, Mr. de Blasio has extracted concessions on affordable housing and workers’ wages from major developers accustomed to V.I.P. treatment from his predecessor, Michael R. Bloomberg, who preferred hand-holding, not arm-twisting.