New Jersey residents who need help paying their rent have until Monday, July 25 to enter a state lottery for housing assistance. 

But the Department of Community Affairs, which administers the program, said that in the last week it had already been inundated with far more pre-applications than it can grant via available slot, underscoring the state’s housing affordability crisis. 

“We are aware of the critical need for affordable housing in New Jersey and remain committed to investing in programs that help to make New Jersey more affordable to live and raise a family,”  Lt. Gov. and DCA Commissioner Sheila Oliver said in a statement this month. “If you are in need of housing assistance, please take this opportunity to submit an application during the open enrollment period.”

The department said 4,000 households will be selected for the Rental Assistance Program, which subsidizes rents for very low income families and individuals, which the state defines as those making less than 30% of the median family income for their counties. The application lists specific income requirements for each county.

As of Monday — a week after applications opened — 61,509 were received, DCA spokeswoman Gina Trish said. And the open enrollment period still had another week to go.