How much for defense?

The Democratic House fired the opening volley in the budget battle by passing a 1984 spending plan that is stingier to defense and more generous to domestic programs than any since President Reagan took office.

For the next weeks the country can brace for crossfire as Mr. Reagan goes to the American public for support of the military buildup and domestic build-down that have been the keystones of his presidency.

Shortly after Reagan delivered a major address Wednesday on the threat of Russian military supremacy, his top defense official gave a stern warning overseas. The House-passed military budget ''would seriously weaken the campaign we have under way now to rearm America,'' Defense Secretary Caspar W. Weinberger said during talks with Spanish officials in Madrid.

Mr. Weinberger punctuated his remarks on the House action with words such as ''very, very damaging'' and ''very dangerous.''

''I think this is the kickoff of a coordinated effort,'' says an aide to Senate budget chairman Pete V. Domenici (R) of New Mexico. ''And the pressure will be on the Senate Budget Committee.''

The Republican-led Senate was poised to write its version of the budget last week when the President persuaded it to wait, in part because the GOP senators indicated they would give only a 5 percent real increase for defense. The White House is seeking a 10 percent hike.

Now that the House has passed an increase of less than half the President's proposal, the pressure will be greater on the Senate to go higher. But as Congress breaks for Easter, members of both parties doubted that the pressure would push the Senate very far. ''I still think the Budget Committee will come close to 5 percent,'' says the Domenici aide, but he and others on Capitol Hill, including majority leader Howard H. Baker Jr. (R) of Tennessee, predict the full Senate will settle on 7 percent.

''It always has some effect,'' said Sen. Lloyd Bentsen of the President's public campaigns. But the Texas Democrat told a breakfast meeting of reporters Thursday, ''He's not about to see 10 percent.''

While the President took his case to the public, House Speaker Thomas P. O'Neill Jr. (D) of Massachusetts argued that the House budget vote Wednesday shows that the public has moved to the Democratic side. The House ''responds to the will of the American people,'' he said, adding, ''The people believe that Reagan policies are unfair and have gone too far.''

For the speaker, the budget victory is the first in three years for his leadership and proof that his party has regained control of the House since picking up 26 seats in the midterm elections.

In the past two years conservative Democrats and the GOP joined hands to roll over the Democratic leadership on budget matters. This year, only 36 Democrats strayed on the budget resolution, and the leadership picked up four GOP votes.

The new Democratic freshmen proved to be, as earlier advertised, ''true'' Democrats. Only six of the 58 voted against the Democratic budget.

The $863.55 billion budget that the House approved this week would raise spending by about $20 billion more than the President's request and increase taxes by nearly $30 billion. It calls for boosting defense by $1.6 trillion over five years, instead of $1.8 trillion sought by the Reagan administration.

On domestic spending, it would restore funding for such programs as child nutrition, food stamps, and welfare by $1.5 billion. So-called discretionary programs, which have been the target of two years of Reagan cutting, would have an influx of money ranging from $8 billion for compensatory education to $2 billion for job training and $308 million for the Environmental Protection Agency.

The highly partisan Democratic budget still must be reconciled with the Senate version to be written next month, however. And many of its most ''liberal'' aspects, including tax increases and some domestic spending, are expected to be moderated.

''I think everybody knows there'll be changes in this budget in conference,'' says House budget chairman James R. Jones (D) of Oklahoma.