On the night of Sept. 8, Gina M. Raimondo, a financier by trade, rolled up here with news no one wanted to hear: Rhode Island, she declared, was going broke.

Maybe not today, and maybe not tomorrow. But if current trends held, Ms. Raimondo warned, the Ocean State would soon look like Athens on the Narragansett: undersized and overextended. Its economy would wither. Jobs would vanish. The state would be hollowed out.