PROVIDENCE, R.I. — Rhode Island is in the midst of an especially grim economic meltdown, and no one can pinpoint exactly why. The smallest state, it is saddled with some of the nation’s biggest problems: the second highest unemployment rate, at 10 percent, according to the latest federal figures; and among the highest foreclosure rates, widest budget gaps and most-vulnerable pension systems. Rhode Island is arguably the most economically hobbled state after Michigan [...]. ... Gov. Donald L. Carcieri, a Republican, and the overwhelmingly Democratic General Assembly have often found themselves at loggerheads, with the legislature more focused on supporting...