I believe we're experiencing one such parallel right now. As many have observed, the U.S. Congress is operating—or rather, not operating—at near historic levels of dysfunction, culminating in the current "fiscal cliff" debacle. (Today, three days before the cliff, the Capitol is empty. Really?) If no deal is struck, as the Economist notes, the ensuing spending cuts and tax increases could easily push a weak economy back into recession.
Compare that to the account we read in Helaman of another ineffective government (about 50 B.C.):
And it came to pass that because of so much contention and so much difficulty in the government, that they [the Nephites] had not kept sufficient guards in the land of Zarahemla; for they had supposed that the Lamanites durst not come into the heart of their lands to attack that great city Zarahemla. (Helaman 1:18, emphasis added)Today, the danger is another recession, not an attack from the Lamanites (although the cuts will drastically affect the military as well). The root cause of those dangers, however, is the same: a dysfunctional government leaving its people vulnerable to great harm.