When New York lawmakers return to the State Capitol next month, one theme will be prominent: President-elect Donald J. Trump’s victory in November.

Their focus will not solely be guarding against what a Trump administration and Republican-led Congress may do that conflicts with New York’s well-being. They will also need to confront the issues that led Mr. Trump to make giant inroads among New Yorkers, even though he failed to win the state in the election.

Gov. Kathy Hochul, a Democrat, has focused on voter concerns in recent weeks as she begins to lay out a re-election argument ahead of the 2026 governor’s race. Legislative leaders say that they have long prioritized these issues, pointing to measures they passed to reduce the cost of housing and child care.

They say that work will continue at pace again next month.

“Over the last couple of years, we have pumped so much more money into child care,” Carl E. Heastie, the Assembly’s Democratic speaker, said in an interview.

“It is one of the ways we have really kept money in the taxpayers’ pockets,” he continued. “But I would say, unfortunately, that is not what we were out telling the voters of the state of New York. Most of the campaign was ‘Trump is terrible.’ And abortion — he wants to take away a woman’s right to choose.”

Mr. Heastie said those are very “important issues,” but “when people are struggling to pay their bills, that stuff kind of becomes secondary.” He said that Democrats needed to continue to do more to bring down costs and emphasize it in their messaging.