Deborah Dailey nestled her 5-month-old son, Nathien, into his baby jumper as they played together at home. Dailey is a child care educator and can't go back to work because she can't get a voucher.

Lawmakers had originally aimed for $250 million to fund the Housing Voucher Access Program, which would subsidize the cost of leases for low-income New Yorkers, but Hochul maintained for years that ...