Democratic leaders of the House searching for ways to cut taxes, cut their losses and rejuvenate the party's ideological roots all at once have given the appearance now and then of branching out in different directions.

But the key to understantding the oatest round of intra-party politicking at the top -- and perhaps the key to the future leadership of the House -- has not so much to so with branches and roots as it has with the ability to tell the forest from the tree, at least as Ways and Means Committee Chairman Dan Rostenkowski sees it.

"Tip O'Neill is the oak and I am the palm," says Rostenkowski, who received his political greening in the arboretum of the late Mayor Richard J. Daley of Chicago.Rostenkowski is a gregarious granite slab of a politician who seems about as much like a palm as Primo Carnera seemed like a prima ballerina, but men of his stature are free to make their own metaphors, and so Rostenkowski goes on to explain the difference between himself and House Speaker Thomas P. (Tip) O'Neill (D-Mass.).

"Tip stands solid like an oak because he's got a basically liberal chemistry and he's got great pride in protecting what has been built in the last 30 years by the Democratic Party.

"I'm still at liberty to be the palm. I can sway."

And so for the past couple of weeks, as his House colleagues watched with interest in the present and an eye toward the future, Rostenkowski swayed.

He swayed with the breezes of compromise when they were wafted on the Senate side by Finance Committee Chairman Bob Dole (R-Kan.). He swayed again when these breezes of compromise were fanned just outside the Oval Office doorway by optimistic whisperings from White House chief of staff James A. Baker III.

He swayed each time with ease, because he is a man whose politics are rooted primarily in the ideology of winning. He spoke of how he wanted to be able to construct a tax-cutting bill in his committee that could win on the House floor. One that would have sufficient appeal to traditional liberal Democrats and those southern conservatives who are also traditional Democrats but who have taken once again to enjoying southern comfort by voting with a Republican White House.

But each time Rostenkowski swayed and spoke in the last couple of weeks, he found himself up against the snow-capped eminence of his close friend and possible future benefactor, Speaker O'Neill, cautioning him against straying too far from the liberal fold that has made the Democratic Party what it is today.

So there was this colloquy of sorts between the two golfing buddies after their session with President Reagan and his top aides this past week. O'Neill was laying on the liberal line: "His [Reagan's] tax is a windfall for the rich . . .creates tremendous debt . . .I don't consider that he made concessions."

And, shoulder to ample shoulder, there was Rostenkowski: "What I find is that there are concessions . . .I did not recognize any door closed."

O'Neill: "When I left the White House I did not appreciate that the door was still open." And in a grand forensic burst worthy of the great W.C. Fields, he added a final fulmination: "I think they are bubbling eppervescent [sic ] with smugness."

The debate over the shaping of a tax cut has been conducted on the House side amid undercurrents that reach beyond the issue of economics to concerns about just who will lead the House Democrats in the years to come. "'m around here to stay," O'Neill proclaims in tones that are loud and firm to signal the strength of his conviction. "Anyone who challenges me must be prepared to roll up his sleeves and fight, because no one has more friends around here than I have -- and that includes among the younger members."

The speaker has already announced that he certainly intends to run for reelection in 1982, but there are still those in the House who figure that he would say that now whether he really intends to run again or not. The prospect of almost two years of lame-duck speakership is far from appealing. And so the undercurrents continue to flow.

Majority Leader James C. Wright Jr. of Texas has strong ambitions to succeed O'Neill, should the speaker opt for retirement. And in the struggle over the tax cut, he was among the strong and public advocates of seeking a compromise measure rather than sticking with a liberal line and suffering another defeat (after the budget fight) on the House floor. Other possible seekers of the job include Democratic Whip Thomas Foley of Washington and House Budget Committee Chairman James R. Jomes of Oklahoma -- who is the man who made the fight for a Democratic budget alternative this year, only to see his principles stampeded by the rush of the southern boll weevils who preferred to vote with Reagan.

Rostenkowski, meanwhile, is also high on every list. A number of House Democrats think, in fact, that if O'Neill were ever to retire he might well like to throw his support behind Rostenkowski as one final act of friendship and regional politics.

Those close to Rostenkowski maintain that because he is also a good friend of Wright's (in fact, Rostenkowski ran Wright's in-House campaign for his present leadership job), he will not challenge him for the speakership, should a vacancy occur. This is also the view of Wright. Interestingly, it is not echoed by Rostenkowski.

"That's a long way of to consider," says Rostenkowski, who would rather talk about future tax cuts than future leadership wrangles, but who answers the question about challenging Wright when it is pressed upon him. "He's my pal -- a good guy." But, always a man who practices his politics Daley, Rostenkowski adds:

"Anyone who lives in the city and doesn't want to be mayor shouldn't live in the city. And any House member that doesn't want to be speaker -- well, you know what I mean, you want to rise to the height of your profession. Be the best.

"But for now I got a lot to prove as Ways and Means chairman. I got a lot to prove yet."

Among the things Rostenkowski figures he has to prove is that he can avoid suffering defeat in his first major action as chairman of the committee that traditionally writes America's taxes. The Reagan White House has opted to fight rather than compromise on something less than a three-year tax cut, mandated in the mode of the original Kemp-Roth plan.

As of now, the Democratic leadership says it is locked in a tough fight -- "Tip doesn't want to be accused of throwing the towel in too early on this one," says one Democratic leader in the House. "He still feels it from the way he got stung on the budget rersolution just for telling it like it was."

But the private assessment of a number of key House Democrats is that the president will probably win this fight, too. He will probably win it even though the principles involved are far from the same. In the budget fight, southern Democrats were lured to Reagan's side because they wanted to trim the deficit. But in the tax cut fight, Reagan's three-year plan for cuts totaling 25 percent would mandate a larger deficit than would that of the House Democrats' plan for two years of cuts totaling 15 percent.

a number of House liberals had pressed Rostenkowski for a bill providing no more than a one-year tax cut, conceding that the measure could never carry the House floor, but accepting defeat over principle as a badge of honor.

But Rostenkowski, reflecting the frustration of compromise efforts that were failing, finally said at one point during a closed meeting of committee Democrats: "Look, I want a tax bill that can win. . . . I don't do anything that I don't fight to win and I never started a fight that I don't fight to win. Understand the economic problems we face. Understand how many hours I have tried to work out a solution with all sides. Understand that we are going to have to come to some conclusions and that everyone is going to have to yield."

In the end, the Ways and Means Democrats agreed to their two-year plan, complete with a number of sweeteners. Some, such as the elimination of the marriage penalty, would skew the tax cuts more toward those in the middle-income brackets. Others, such as the relief on estate and gift taxes, will appeal to rural Democrats whoe constituents suffer from inheritance laws that do not compensate for the effect of inflation on farm land and equipment.

The committee Democrats voted in near unanimity (there is only one defector to GOP ranks) and burst into applause when the deed was done. But it became apparent to them soon that there was more to it than met the ayes. Because the Reagan bill contained virtually the same sweeteners -- and these sweeteners have attracted the boll weevils to the Republican bill like cotton candy.

"When they had the pure Kemp-Roth and the 10-5-3 (depreciation plan) we had them licked and they knew we had them licked," says Tip O'Neill. "But where we made our mistake was . . . in allowing them to get the information of what was in our bill -- the sweeteners. They took everything we want. They took the goodies that were under our table."

EPILOGUE: Late Thursday afternoon, with the prospects of his committee's tax-writing effort very much in doubt and the frustrations of being chairman weighing heavily upon him, Rostenkowski reflected upon what it means to be chairman of Ways and Means. It means, in the eyes of some, that he will be considered for other leadership jobs -- such as speaker. It means, in the eyes of others, that he is a big man in the planning of the nation's economy, win or lose on the tax cut.

But it also means something else that is very important, he said.

"It means that there are all kinds of people throughout the business community who take very great care to pronounce my name correctly now.

"They used to see it on a piece of paper, and they'd get all like this (he molds furrows of frowning into his forehead), and they'd say 'Rostokop . . . Roskotow . . .' or they wouldn't bother to say anything at all.

"Now they say it very carefully: 'Ros-ten-kow-ski.'"

He savors it, says it again, then lifts his hands toward the ceiling of his office as though pointing at someone.

"They say 'Rostenkowski!' My old man would be up there on top of the church steeple, if he could hear how carefully the say it now!"