MINEOLA, N.Y.  Facing a huge budget deficit when he took office in January, Nassau County Executive Edward P. Mangano did not impose a hiring freeze. He did not stop borrowing to subsidize some of the richest school districts in the country. He did not eliminate the Police Department’s beloved mounted unit.

Instead, Mr. Mangano, a Republican who won one of the first upsets of the Tea Party era, did what he had promised: He cut taxes, adding $40 million to the county’s deficit, which has since reached nearly $350 million.

Now, with its bonds suddenly downgraded and a state oversight agency preparing to seize its checkbook and credit cards, Nassau is on the verge of a full-fledged fiscal crisis.

That things could get so dire in this wealthy county, where property taxes are the second highest in the nation, offers a lesson in what happens when anti-tax fervor meets the realities of disappearing revenues and a punch-drunk economy. At heart, though, the situation  like state budget crises in New York, New Jersey and Illinois  illuminates the troubles long-prosperous governments, with established interest groups and residents accustomed to high levels of services, face in adapting to protracted lean times.