The nation’s governors have sounded a similarly bleak note: New York’s Andrew M. Cuomo, a Democrat, and Maryland’s Larry Hogan, a Republican, said in recent days that states need about $500 billion in federal aid, or they will have no choice but to consider steep reductions in government programs at a time when local residents need help most. In Michigan, for example, the budget shortfall may be as high as $7 billion over the next 18 months, a staggering cost for the state and others like it still reeling more than a decade after the last economic downturn.