The day after Gov. Kathy Hochul announced the framework for a $254 billion budget for New York State, she sought to deliver a celebratory message in two parts.

She visited a preschool and then dropped by the Albany County district attorney’s office, with each stop on Tuesday serving a distinct purpose. To prosecutors, she highlighted how she fought for changes to so-called discovery laws, decreasing the chances that criminal cases might be thrown out because of “some technicality.”

At the preschool, she reiterated how the budget, whose passage is now one month late, had become her fight for families. “I said it back in January that this budget will not be completed until I can provide relief for struggling families,” she said.

State budgets have always provided a fiscal road map for the priorities of the governor and state legislative leaders. But in New York, the budget can also be a blueprint for an assortment of political imperatives, from criminal justice changes to cellphone bans in public schools.

And for Ms. Hochul, who is expected to face a hotly contested re-election next year, the messaging behind the budget — “your family is my fight” — may well be a preview of her campaign strategy and perhaps one that Democrats might follow in next year’s midterms. Here’s a closer look at the budget agreement, which still awaits bill language and formal passage.

Steps to make New Yorkers feel safer

Few things haunt Ms. Hochul and her re-election chances more than outsize attention to a random act of violence in the city’s subway or streets.