In the champagne celebration in the Oval Office after the Reagan administration's landmark victory last week, an aide commented to White House counselor Edwin Meese III that the president's personal efforts on behalf of his tax bill had been phenomenal.

"Yes," Meese replied. "It was like the work he did to get the welfare bill in California. He really wanted this one."

The Sacramento reference by the man who was President Reagan's executive secretary during most of his eight years as governor was a timely reminder that the 70-year-old who occupies the White House was not born yesterday in politics.

When Reagan came to Washington, he was told by House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) that his experience in California had been "minor league" and that he was now in the majors.

In fact, Reagan's ability to hit big-league political pitching rather consistently was polished in the fast company of the nation's largest state government, where he struck out a lot during a 1967 rookie season and seemed for a time to be a flash-in-the-pan governor.

"He'll never understand the legislature," one of the state's most prominent Republican legislators predicted several months into Reagan's first state legislative session.

It was the same sort of judgment Democrats in Washington made at frequent intervals during the past four years about President Carter's understanding of Congress. But they are not likely, after this season's spectacular presidential triumphs, to belittle Reagan's grasp of Washington politics.

Reagan trhives on being underestimated. After his election last fall, the conventional wisdom in Washington, celebrated in The Washington Post as well as on the floor of Congress, was that Reagan would quickly run up against the ralities of an opposition House and a dug-in bureaucracy and, like presidents before him, turn his attention to foreign affairs, where chief executives are less impeded by votes.

Others thought he would be diverted from his economic agenda by ideological considerations, especially the "social issues" dear to the heart and wallet of the Moral Majority.

Six months later, that conventional wisdom is ruined and discredited. Reagan the politician stuck to his first priority, the economic recovery program, and forced a new agenda on the existing political order. Democrats found themselves beaten again and again by the combined public-private skills of his video presence and his shrewd tactical bargaining for marginal votes.

What Washington still may not comprehend fully is that Reagan has succeeded so far as president less by learning from Jimmy Carter's mistakes in Washington than from his own in Sacramento.

While Reagan started out in political office as an aloof celebrity content to soar above the political battleground, he learned gradually how to focus his personal charm upon the lowly riflemen of politics: the assemblymen and congressmen who have to vote each day and give their constituents a plausible account of their actions.

Reagan started out as a nonstop talker intent on giving politiciansthe same speech they had heard rom the stump, but he learned in time to be a listener. Instead of telling people what he wanted them to do, he learned to ask them for their support.

In political negotiaitons, he started out by pooling his ignorance on measures his listeners usually understood far better than he, but Reagan has become powerfully informed on the issues most important to him.

It is too much to say, on any issue, that Reagan become a detail man. But his grasp of legislation, once primitive, has become more sophisticated, and he was able to discuss the budget and the tax bills without interpreters.

Just how much Reagan hs learned was illustrated by a conversation last Thursday among three House members who had attended Reagan's speech to a conference of state legislators in Atlanta and were accompanying the president back to Washington on Air Force One.

The congressmen represented the gamut of Reagan's support on his budget and tax bills: Next Gingrich, the only Republican House member from Georgia; Billy Evans, a "boll weevil" Democrat from Macon, and Frank Horton, a veteran upstate New York Republican congressman and member of the moderate coalition known as the "gypsy moths."

All agreed that Reagan was the most effective presidential leader they had encountered, and that he had been especially impressive in winning the support of Congress.

Horton praised Reagan for being "a listener" when he met with congressmen, "unlike mot presidents." Gingrich, expanding on the point, said the White House had engaged in real teamwork with the House Republican leadership. Evans said he had no problem supporting Reagan's economic proposals as a Democrat, because conservative Democrats had been given an opportunity to help shape the tax bill.

And so it went. These congressman were talking, admiringly, on the gut level of practical politics, but the same point was made in larger form Friday night by William P. Bundy, the editor of Foreign Affairs, in a speech to a policy study seminar.

". . . The president has shown both a capacity to speak persuasively to the American people and a skill and organization in dealing with Congress that have not been seen in Washington since at least the days of John Kennedy or the Lyndon Johnson of 1964-65," Bundy said.

"Morever, whereas Kennedy could speak but not twist arms , and Johnson could twist arms but not speak, Reagan it appears, can do both, perhaps to a degree for which one would have to go right back to Franklin Roosevelt for a parallel, and in a way that hits observers all the harder as it comes after a president who could do neither."

Even on foreign affairs, which is supposed to be Reagan's weak point and where Bundy found the president lacking in the prestige of Eisenhower or the grasp of Kennedy or Nixon, "Both potential domestic critics and foreign statesman have seen a combination of personal charm and firmness of purpose that are bound to make them think twice before taking him on, at least head to head. . . ."

It has become fashionable to call Reagan "the Great Communicator," and that is certainly a part, a large part, of his effectiveness.

"We thought we were beat on the tax bill," said White House chief of staff James A. Baker III. "Then the president just blew them away in a speech, and the American people responded, and we won. It sounds cornball to say it, but that's what happened."

But it is not Reagan's skill as a communicator alone that is responsible for what has happened in the last six months. In the after-speech discussion of Horton and Gingrich much credit was given to legislative liaison Max L. Friedersdorf and to budget director David A. Stockman.

Others in the administration point to the strategic direction of the little-known White House "legislative study group," where such unheralded but important White House aides as Richard Darman joing Baker, Stockman and deputy chief Michael K. Deaver in making decisions.

This cast alone is symbolic of the Republican diversity within the White House. Friedersdorf was a Richard M. Nixon and Gerald R. Ford man, Baker the campaign manager for Ford and George Bush, Darman a protege of Elliot L. Richardson, Stockman a bright and independent conservative congressman, Deaver a trusted aide of Reagan.

"The president's personal security had a lot to do with making his administration possible," said a Reagan friend who did not become a member of the government. "He kept people around him he trusted, then reached out for others. He was not afraid to seek advice. He wanted very much to be a successful president, to carry out what he was elected to do."

It is this powerful focus, more than anything, that is reminiscent of Reagan's first political hero, Franklin D. Roosevelt, and which has made him an effective president.

None of this suggests that Reagan will not encounter painful defeats in the months ahead. He faces difficult decisions on strategic defense options and future budget cuts as great as the ones enacted this season.

His most recent news conference demonstrated that he is sometimes close to no-man's land on foreign policy. There are, as Bundy observed, conflicting ideological and pragmatic tendencies in approaches to other nations.

But Reagan has demonstrated once again in these first months of his presidency that it is always dangerous to underestimate him. This is not some Hollywood cowboy who has settled into the White House for early retirement, but a dedicated and serious politician who knows how to grasp the levers of power in the age of television. Reagan plays big-league politics. Even Tip O'Neill knows that now.