The State of Illinois is still paying off billions in bills that it got from schools and social service providers last year. Arizona recentlystopped paying for certain organ transplants for people in its Medicaidprogram. States are releasing prisoners early, more to cut expenses than to reward good behavior. And in Newark, the city laid off 13 percent of its police officers last week. While next year could be even worse, there are bigger, longer-term risks, financial analysts say. Their fear is that even when the economy recovers, the shortfalls will not disappear, because many state and local governments have so much debt — several trillion dollars’ worth, with much of it off the books and largely hidden from view — that it could overwhelm them in the next few years.