Head Start programs that serve tens of thousands of the nation’s neediest preschoolers are facing a cutoff of federal funding at the end of the month because of the government shutdown. That would leave many programs scrambling to figure out how to keep their doors open. The early education initiative is funded almost entirely by the federal government, making it particularly vulnerable to funding disruptions. The programs are run by schools, local governments and nonprofits. The programs receive new grants annually and are not allowed to carry over unspent money.