In a move highlighting the severe fiscal stress facing many states, New Jersey officials have been negotiating a temporary bank loan of as much as $2.25 billion to plug a cash shortfall, according to people familiar with the matter.

The loan would cover bills the state will need to pay as its new fiscal year begins July 1. Normally, states have some cash available as they finish one fiscal year and begin the next, while gearing up for a bond offering based on the new budget.

New...