NEW YORK — Now that state lawmakers have closed a budget deal to fund prekindergarten in New York City, Mayor Bill de Blasio is ready to turn to the next items on his sweeping liberal agenda: massively expanding affordable housing, increasing wages for the working class and overhauling the city’s recovery from Superstorm Sandy.

De Blasio’s road ahead, confirmed by the mayor and his senior aides, is an attempt to tighten the focus around his campaign theme of combatting income inequality and to steady an administration that has seen its poll numbers shrink in the first 100 days, thanks to a series of unforced errors and grueling battles with Albany.