The reason none of the states have any federal resources to deal with the influx of migrants is because Donald Trump defunded all federal immigrant support services and cancelled all programs for housing, jobs and legal services, in favour of arrest and detention of anyone crossing the border. Once these services were gone, and the staff disbursed to other NGO's or jobs, assessing the needs and rebuilding service takes time.
The Biden Administration offered to work with border states, to meter entries so they weren't overwhelmed, and to direct funds and resources to where they were most needed.
Greg Abbott and Ron DeSantis flat out refused to even discuss their issues with the Biden Administration, or to cooperate in rebuilding the resource network for incoming migrants. They just started tricking incoming migrants into getting on buses and planes and shipping them out of state. This cruelty, inflicted on people who are just trying to find hope and safety, was inhumane and despicable. It was also violated their Constitutional rights.
The New York Mayor is rightfully saying, "We need more resources". And the Biden Administration immediately started working with him to provide them. That's what government is supposed to do. Not abuse poor people for political theatre.