President Reagan offered the American people yesterday another snapshot of the kind of government he has struggled to create for five years: an expanding military and a shrinking federal role in everything from farming to housing to travel to college education.

Reagan's priorities are certain to be challenged by Congress in the weeks ahead. But the fiscal blueprint he unveiled for next year underscores the larger imprint Reagan would like to leave on the government in the final years of his presidency.

That outlook places heavy emphasis on defense, foreign aid, drug and law enforcement, and protecting U.S. embassies against terrorism. But it views the government as having little or no role in making loans to small businesses, subsidizing intercity passenger train service or regulating the truck and bus industries, among other things.

What has been a common theme in every Reagan budget since 1981 was renewed in yesterday's spending plan: Reagan has not so much shrunk the overall size of government as reordered the priorities within it.

In the new budget, he suggested about $23 billion in domestic program cuts for next year while adding about $33 billion to national defense.

While it may never become reality, this proposed shift in priorities has already become the fulcrum of political debate over the budget.

"To carry out his view of what the defense establishment should look like, he's fully prepared to steal from future generations, and to rob every other segment of our society to accomplish that," said Rep. George Miller (D-Calif.). "He has made it very clear he is in no way prepared to pay for the military buildup other than taking it out of the hides of the rest of people served by government."

Lawrence A. Kudlow, former economist at the Office of Management and Budget during Reagan's first term, said the president is trying to use the new balanced-budget law as a "club" to "preserve defense as much as possible and sacrifice the nondefense budget."

Reagan has constantly pursued this goal, but from different angles.

As a candidate in 1980, he talked of eliminating "waste, fraud and abuse." Once elected, he opened a full-scale attack on domestic programs that benefited the poor, and was partly successful, despite resistance in Congress.

Later in his first term he tried other approaches.

As a candidate in 1984, he simply avoided all talk about the painful domestic cuts, and promised that economic growth would melt away the deficit.

The budget he submitted to Congress yesterday frankly confessed that promise was untrue: "It is incorrect to assume that economic recovery will, by itself, reduce the deficit."

Last year he targeted what former budget director David A. Stockman called the "six sob sisters of subsidy," mostly federal aid to the middle class and business.

This year's effort employs a new set of tools in addition to leftover ideas from last year.

Reagan is proposing to "privatize" many government functions such as regional power marketing and crop insurance, turning them over to private business, and is resuming his quest for "federalism," transferring highway and transit programs to state and local governments.

He is once again trying to tack on higher "user fees" for such federal services as Coast Guard assistance to private boat owners or admission to national parks.

And he is proposing outright elimination of other federal programs, even though Congress voted last year to keep them, including Amtrak and the Small Business Administration.

Reagan's fiscal 1987 proposal was sprinkled with statements of philosophy behind these moves. In justifying reduced federal transportation subsidies, for example, the fiscal plan says "support of essentially local activities is not an appropriate federal role," and that mass transit projects such as Washington's Metro system have been "unnecessary, too costly and underutilized."

The federal government, it says, "should get out of the business of paying for local sewage treatment systems, local airports, local law enforcement, subsidies to state maritime schools and local coastal management."

Reagan's hope of casting off many government functions to private business and local governments is also driven by another factor -- the deficit targets in the balanced-budget law Congress passed last year. To reach the $144 billion target in the budget he submitted yesterday without raising taxes, the president had to find $38 billion in deficit savings.

Of that total, $6 billion comes from new revenues, chiefly Reagan's acceptance of an 8-cent-per-pack tax increase on cigarettes which he once opposed. Another $5 billion comes from user fees and other charges, $3 billion from slightly slower defense growth and $1 billion from lower interest on the national debt.

The remaining $23 billion represents reductions in program, some of which benefit the poor, such as subsidized housing and Medicaid.

Reagan also identified a few "high-priority" goals beyond defense. One was to build up the air traffic control system with new controllers and safety inspectors. Another was a major increase in foreign aid; a third was to improve security at U.S. diplomatic installations overseas.

Reagan also calls for additional money for the Drug Enforcement Administration and Federal Bureau of Investigation to fight illicit drug trade, for expanded space exploration, for basic scientific research and for research on acquired immune deficiency syndrome (AIDS). In this case, however, Reagan's proposed spending of $213 million falls short of the $244 million Congress voted in 1986.

But the biggest priority remains military expansion. Among other things, Reagan seeks a major increase for research on his proposed missile defense system, the Strategic Defense Initiative, and a doubling of the budget for the small, mobile ICBM known as Midgetman about which some in the administration have expressed doubts.

Many in Congress and the administration have acknowledged that Reagan will probably fall short once again in his defense spending plans, but he has succeeded in changing the terms of the debate.

"He has gotten Congress and the country to focus on the deficit and used it as a club to beat down social spending, but he never put the savings from the cuts against the deficit," Miller said. "He only used them to increase military expenditures. He has played Congress like a fine fiddle, and they've bought into this notion year after year, and this is where we are."

Reagan has pushed Congress closer to his priorities every year by holding fast against compromise until the last possible minute. But this year, the new balanced-budget law has increased the risks of this tactic. If Reagan and Congress reach stalemate over fiscal priorities, the law sets in motion automatic spending cuts that will seriously erode Reagan's military buildup, perhaps far more than is currently being demanded by his critics in Congress.

"Everyone understands the stakes are much higher," said Kudlow, who called the new Gramm-Rudman-Hollings law "Grambo" and predicts it would force an early compromise on fiscal priorities between Reagan and Congress.

He added, "I think you will see this ritual played out in shorter form this year. I don't think you will see Reagan go to the mat on defense as he has in prior years. I think the handwriting is on the wall, and it spells 'Grambo.' "