A huge federal deficit, chronic high unemployment and other long-term ills face Canada in 1985 as newly elected Prime Minister Brian Mulroney reverses the policies of his predecessor and beckons anew to the United States for investment dollars that could create jobs for a stagnating economy north of the border.

Although such major questions as French-English bilingualism, bilateral relations with Washington and the nation's role in NATO remain at the top of any Canadian leader's agenda, national economic problems head Mulroney's list as he explores his political mandate.

Ottawa's deficit stands at $35 billion -- barely more than a drop compared with Washington's bucket of federal red ink. But the deficit has made Canadians uneasy about their future prospects, and no wonder: Interest payments on the debt siphon 22 cents from every federal dollar. In a country that prides itself on balancing federal thrift with a strong commitment to social services and welfare, the question of debt reduction has important implications for the prime minister.

The Conservatives rang up a whopping 211-seat majority in the House of Commons in last September's national election, bringing an emphatic end to the 16-year era of Pierre Trudeau. In a stunning reversal of fortune, the Liberals, who dominated Canadian politics throughout this century, have been reduced to a tiny 40-member parliamentary minority; they are struggling hard simply to stay alive politically.

These circumstances ensure the jut-jawed, 45-year-old lawyer-businessman plenty of parliamentary muscle as he deals with the economy. Mulroney has a particularly Canadian cross-cultural heritage: of Irish descent, he grew up in a blue-collar Quebec mining town and is completely at home with both French and English.

Because of Canada's historic xenophobic reactions to the economic power of the colossus to the south, Mulroney's gesture to American investors is politically adventuresome. But it is also explainable in more personal terms: He gained cross-border business experience as president of the Iron Ore Co., a Canadian subsidiary of an American company.

The moves also underscore the fact that Mulroney's options in dealing with economic malaise are limited at least as much by the structure of his nation's economy as by any other factor. What looked like plausible opportunity for change during the campaign may now look more like a burden buoyed by no easy solutions.

Canada is unique among advanced industrial nations, earning more of its way in the world by producing and selling natural resources -- such as timber, minerals and energy -- than any other member of the group. The nation is extremely vulnerable to short-term fluctuations in worldwide commodities markets. At the same time, Canada has not kept pace with other developed nations as they embrace high technology.

According to a recent study of global economic competition by the Canadian-American Committee, the restructuring of the world's economy and the emergence of Third World competitors has hit hard at the natural resources sector of Canada's economy. Just 25 years ago, minerals, timber, basic metals and energy accounted for 65 percent of Canadian exports. In 1981, that traditional economic backbone had shrunk to 40 percent.

In part because of this, the robust economic recovery that got under way in the United States during President Reagan's first term has not been matched in Canada, where stagnation continues.

The Canadian GNP is expected to grow this year by 2 to 4 percent, respectable enough after the severe recession of the late 1970s but unlikely to have significant effect on the 1.3 million unemployed. Most of the country's factories are operating below capacity, and capital investment projections for the year fall well short of achieving more than piecemeal replacement of aging machinery and manufacturing plants.

Faced with this unpromising picture, Mulroney has moved to reassure American financial managers that U.S. investment in Canada is once again welcome. "Canada is open for business again," he told an applauding, black-tie audience of the Economic Club of New York last month. "The government of Canada is there to assist, and not harass, the private sector in creating new wealth and new jobs that Canada needs."

Trudeau's old Foreign Investment Review Agency, which was intended to screen Canada from excessive investment from the United States, is being renamed Investment Canada by the Tories. As outlined by Mulroney in his Economic Club speech, its mission will largely be limited to reviewing direct foreign takeovers of Canadian enterprises worth more than $5 million.

Lifting investment curbs may have an effect on the nation's industrial heart, cradled between Lakes Huron, Erie and Ontario in southwestern Ontario Province. The region is Canada's richest job market, producing about 40 percent of the annual GNP. But elsewhere, prospects for any quick recovery remain less promising.

The Maritimes, where unemployment is as high as one in five (Newfoundland), remain deep in the doldrums. The U.S. breadbasket's farm troubles are duplicated in Canada's wheat-growing provinces as well. The western provinces have been hit by troubles in their key timber and paper industries, and the continuing world energy glut has added its own woes in these energy-rich provinces in the form of depressed oil and natural gas prices.

To help stoke energy exploration in the Maritimes, Mulroney intends to scrap the Liberals' National Energy Program (NEP), which gave the government a 25 percent share of any oil found offshore or in the far north. That policy was blamed by the Tories for stifling offshore operations, which, after the second OPEC oil embargo in the late 1970s, might have brought thousands of well-paid jobs to the depressed communities of the Canadian east coast. The oil glut makes it unlikely that abolition of the NEP will have a quick impact on the Maritimes.