"For once, a strategy that was carefully conceived actually materialized," David A. Stockman said this week, his voice betraying both pride and a little awe.

The whiz-kid director of the Office of Management and Budget was talking about the key budget votes in the House that have transformed the political game in Washington. Stockman has been on the covers of the news magazines, starred on television and become a household word in the last six months, "but this is the first real thing that's happened as far as I'm concerned," he said.

Interviews with key players in this Potomac melodrama suggested that Stockman's triumph was more complex than it appeared on the surface. In fact, the "strategy that was carefully conceived" included a good deal of improvisation. Examples:

The final and perhaps gravest obstacle in the House was not the need for two dozen Democratic votes, but the absolute requirement that virtually every Republican support the Reagan program.

For several hours on the day of the final vote, Stockman and the party leadership conducted a disorderly meeting in a room below the House floor to hold the hands of wavering members, particularly about 30 from the Northeast and Midwest who are the most liberal Republicans in the House.

"Only we could have gotten those liberal Republicans to vote for this budget," said a White House aide. "That was a much bigger accomplishment than than getting 26 conservative Democrats to vote for things they usually vote for anyway." All except two Republicans ultimately supported the administration, and one of those, Rep. Claudine Schneider (R.I.), said her vote would be available if absolutely necessary.

James A. Baker III, White House chief of staff and the administration's chief political coordinator, was inclined at one point to accept the proposals of the Democrat-controlled House committees for satisfying the stringent spending limits the House had approved earlier. The risks of defeat if the administration tried to overrule the committees might outweigh the benefits of victory, Baker worried. Stockman's fervent desire to challenge the committees helped convince him otherwise.

On the day of the final vote on the Reagan-backed alternative to the committees' budget-cutting proposals, Rep. James T. Broyhill (R-N.C.), after consulting House Republican leaders, decided to drop his tougher alternative to the spending plans of the Energy and Commerce Committee, thus relinquishing the chance to save an additional $2.8 billion that the administration had sought. This was decided without consulting the White House, according to Max Friedersdorf, President Reagan's director for congressional relations. Broyhill's move may have saved the whole package, White House aides acknowledge.

In the end the administration won "94 percent of the entitlement changes and savings . . . that were proposed in the president's plan in March," by Stockman's reckoning. Stockman and his staff, citing examples of compromise, insisted that the administration had not "dictated" to Congress. But the 94 percent figure still stood.

In fact, the Stockman approach was to negotiate, but only with the liberal Republicans and conservative Democrats he knew were needed for victory. There were no significant negotiations with the Democratic leadership -- no attempt to accommodate committee chairmen or the speaker.

The Republicans' first move came about a month ago, after both House and Senate had approved the budget resolution setting the new spending ceiling and requiring the committees to "reconcile" existing legislation with that ceiling by cutting spending. The House Republican leader, Rep. Robert Michel (Ill.), called together key colleagues and staff to discuss the pitfalls of the reconciliation process. They realized the Democrat-controlled committees would have a chance t circumvent some of the most stringent spending restrictions in the resolution.

Later the same group met with Stockman and decided that, because the final reconciliation legislation would be so long and complex, they should begin at once to draft a reconciliation bill fully compatible with the Reagan program.

At this time, it was widely assumed in the inner circle of the White House that a sbustitute reconcilation bill incorporating the president's budget would be reasonably easy to sell in the House "We underestimated the institutional pride up there," said a senior official.

The substitute proposal was drafted after a period of "endless meetings," as one participant put it. The House Republican leaders and Stockman met group by group with the Republican membership of each committee, analyzing the programs in the jurisdiction of each and identifying the best ways to cut them. Simultaneously, the same leaders were meeting with the liberal Republicans to look for ways to satisfy their needs -- by increasing government aid to Conrail, for example.

At this stage Republicans were assuming that the Democrats would probably try to subvert the budget resolution by using gimmicks to meet its spending targets. But the committees' final products impressed the senior Republicans as much better than they had feared. Some, including Michel, began to wonder if it wouldn't be wiser to accept the committee versions.

Thursday, June 18, was a key day. First at lunch in the White House, then in a meeting in Michel's office on Capitol Hill, Stockman, several key conservative Democrats and the Republican leadership analyzed and analyzed the situation. At first, "the southern Democrats didn't show much stomach for a fight," according to one participant.

"We went uphill and down," this source continued. "Finally some stirring speeches were made" -- by Stockman and Michel -- "and spirits were raised." That long afternoon produced a proposal for a compromise: to accept the bulk of the committees' recommendations, but amend many others, especially for five big entitlement programs.

The next day Stockman had to persuade his senior colleagues in the White House that this was the best way to go. He met with counselor Edwin Meese III, Baker, Friedersdorf, director of communications David Gergen and Richard G. Darman, a Baker associate. All of these men had been paying more attention to the fight over Reagan's tax proposals in the House and Senate tax-writing committees than to the latest developments in the budget fight. Stockman tried to bring them up to speed.

But there was still a political consideration. Baker was nervous about risking the momentum of Reagan's program on a tricky House vote that could too easily be lost.

Controlling the Rules Committee, the Democrats could make it impossible to put the Reagan-endorsed substitute package before the whole House. If this happened, the administrations's friends would have to win a floor vote rejecting the committee's rule governing debate. Baker wondered if it was dangerous to stake the president's standing on this procedural vote.

Stockman argued that if the southern Democrats were allowed to hide behind a procedural gimmicks to avoid an up-or-down vote on the Reagan program, then soon they would be caving in every time Speaker Thomas P. (Tip) O'Neill (D-Mass.) put pressure on them. And that would be the end of any Reagan coalition in the House.

It was decided the issues were too complex and time was too short to press for a TV address. Moreover, no one wished to squander the administration's best public relations man on such a chancy proposition.

Indeed, in the week of the cruicial votes, Reagan, Baker and Meese all left town while Gergen, Darman, Stockman and Friedersdorf helped the House leaders to lobby (Meese returned just before the vote.) Late on the afternoon of June 25 administration supporters defeated the Rules Committee's strategy, 217 to 210.

Victory was confirmed in the final substantive vote a day later. In the last 24 hours liveral Republicans were a bigger worry than the conservative Democrats. "Holding 190 Republicans on vote after vote the way Bob Michel did was a major miracle," Friedersdorf said later.