A hectic three-week campaign began today for Ireland's second national election in just seven months, a campaign that amounts to a referendum on Prime Minister Garret FitzGerald's approach to the problems of the Irish economy and British-ruled Northern Ireland.

FitzGerald's minority coalition government fell last night when independent legislators holding the balance of power in parliament voted against a tough budget that would have deeply dented the pocketbook of almost every voter. The budget was designed to reduce the government's sizable deficit and foreign borrowing with widespread tax increases.

Arguing that the budget was necessary to correct a "horrifying situation" inherited last year from former prime minister Charles Haughey, FitzGerald said, "We are more than willing to fight an election with it as the major issue."

Haughey, leader of Ireland's largest party, Fianna Fail, today called the budget "inhuman, savage and antisocial." He said voters would repudiate the coalition of FitzGerald's Fine Gael party and the smaller Labor Party, which may not stay together during the campaign because of strains over economic policy.

Without FitzGerald's budget, the Irish government would be forced to borrow the equivalent of 17 percent of its gross national product to meet this year's deficit.

The Irish economy suffers from an inflation rate of 23 percent--double the average for the European Community--and a rising unemployment rate of more than 11 percent of the work force. Ireland's economic production has been stagnant the past two years after two decades of rapid growth that abruptly transformed a poor, agrarian society into a modern, industrialized nation.

Many of the new high-technology industries attracted with generous government subsidies have continued to thrive, but agricultural exports have fallen off. Prosperity ended massive foreign migrations of Irish, but it became more difficult to provide jobs for a rapidly expanding working population. Spiraling wage and tax increases fed inflation.

"The experience of growth and the rise in living standards has not prepared our people for the current situation," FitzGerald said in an interview last month in Dublin. "There has been a considerable problem adjusting to what will have to be, for some years, a slight reduction in living standards. People tend to resist that."

Yet FitzGerald said then that "in general, people will understand that there is a major problem. There is a willingness to accept measures that attempt to put it right."

This belief will be tested by the voters' reaction to his budget proposals, which would have reduced take-home pay and raised consumer prices for almost everyone.

FitzGerald said last night he also intended to emphasize during the campaign his record on neighboring Northern Ireland. While he and Haughey have similarly increased cooperation between Ireland and Britain in tackling the problem, FitzGerald has been publicly more conciliatory toward the Protestant British loyalist majority in Northern Ireland.

FitzGerald began a campaign to reform Ireland's constitution by removing both its Roman Catholic Church-supported ban on divorce and its unconditional territorial claims to Northern Ireland. He also has backed an attempt expected to be made soon by Britain's Northern Ireland secretary, James Prior, to gradually establish limited home rule in the province that would give the Catholic, Irish nationalist minority some share of power.