New York collected $2.3 billion less income-tax revenue than predicted for December and January, a development that Gov. Andrew M. Cuomo (D) blamed on wealthy residents leaving for second homes in Florida and other states that received more favorable treatment in the tax law enacted by President Donald Trump and the Republican Congress.

The shortfall will require a new look at the $175 billion budget Cuomo submitted to the legislature last month, he said. If the trend continues, the governor...