(FORTUNE Magazine) – You know about rescuing S&Ls and commercial banks. Rescuing state unemployment insurance funds may be next. Connecticut, hit by a 66% surge in benefit claims, has already asked the federal government for a $227 million loan to tide it over through the end of March. But if the recession becomes severe, another 34 states could be lining up by year's end, caps in hand, looking for help as their funds run dry. How bad is it? The Urban Institute, a nonprofit group, considers it good practice to have 18 months' worth of benefits on hand. But only seven states do: Hawaii, Mississippi, New Mexico, Oklahoma, Oregon, South Dakota, and Vermont. Nancy Lazar, an economist at C.J. Lawrence, a New York City brokerage firm, says that the number of first-time claims will probably rise from 20.6 million in 1990 to at least 26 million in 1991. That would bring them level to claims made in 1980, but below the 31.9 million in 1982, a record year. Says she: ''Typically, the number of claims filed doesn't decline until the economy clearly starts to improve. We're at least nine months away from that.'' The possible shortfall in state funds: as much as $13 billion in total. The U.S. has $3 billion in reserves to cover emergencies. If that goes, Uncle Sam would have to cut other spending. Meanwhile, legislatures might be forced to enact increased unemployment insurance taxes.