Tip O'Neill, labelled a political bumbler hopelessly out of step with the times, spoke on election night as the undisputed leader of the House. Once described as "just like the federal budget -- fat, bloated and out of control," he has had the last laugh: the words are from soon-to- be-ex-congressman John LeBoutillier. O'Neill speaks in the conciliatory language that legislative leaders use when they have confidence that they have the votes.

To understand why he has the votes, you have to understand first that O'Neill was never the bumbler critics claimed. Yes, he lost the budget and tax votes in 1981. But in losing them, he suffered fewer Democratic defections than any Democratic speaker in 40 years. From the body of 242 Democrats elected in 1980, O'Neill lost 48 Democrats on the key tax vote in 1981. Compare that with a historic precedent: Sam Rayburn's victory on the fight to pack the House Rules Committee in 1961. On that one, Rayburn had a House with 262 Democrats and the aggressive support of an administration that wasn't shy about using political favors to win votes. Still, 64 Democrats deserted the speaker on that crucial vote. Rayburn won by five votes, only because he had the support of 22 Republicans. O'Neill, in contrast, got exactly zero Republican votes on the 1981 budget.

The factors that produced this extraordinary cohesion when there were 241 Democrats in the House now give O'Neill sway over a House with 269. They are:

* Fair and prompt procedure. The Republican-Dixiecrat alliance that dominated the House in Rayburn's time did so in large part through control of the Rules Committee. When Rules Chairman Howard Smith didn't want a liberal bill to pass, he would go down to his farm in Virginia for a couple of weeks and not call a meeting. The bill was killed, since bills ordinarily can't go to the floor without Rules Committee action. O'Neill has refused to use such tactics, though he controls the Rules Committee by an 11-5 margin. But he kept the Reagan budget and tax bills on a tight schedule. Now he is in good position to speed legislation he seeks.

* Uniting Democrats, not seeking Republicans. When he became speaker in 1977, O'Neill was leader of 290 Democrats. He promised not to seek liberal Republican votes; he would concentrate on uniting Democrats. That is what he did in 1981. Then there were too few Democrats for his position to prevail. But by letting Republicans achieve unprecedented party unity, he also put on the spot Republicans from industrial Northeast and Midwest districts. This year, several were beaten -- Lawrence DeNardis of New Haven, Conn., James Nelligan of Wilkes-Barre, Pa., Harold Hollenbeck of East Rutherford, N.J. In the next Congress, O'Neill can probably get the votes of 10 Republicans with similar districts on economic issues, without even asking for them.

* Reaching a Democratic consensus. On the budget bill in 1981, the speaker worked with Rules Chairman Richard Bolling and Budget Chairman Jim Jones to get an alternative that would maximize Democratic support. It was far less generous on domestic spending than many Democrats wanted, but it came close to passing. O'Neill followed the same procedure he had used in 1977 on the energy bill: using talented, consensus-minded chairmen, leading a committee broadly representative of House Democrats. The result in both cases got unusually high (231-50) Democratic support. And it gave the House a serious alternative on which it could make a prompt decision. That process, having worked once, will be ready to move again in 1983.

* Party accountability. In his years as speaker Democratic legislators have been accountable to their colleagues -- a vivid contrast from the old days. The change was made after the 1974 elections, primarily by Phil Burton of California, when it was established that all committee chairmen would be selected by secret ballot of all Democratic members. Southerners such as Jamie Whitten, now chairman of Appropriations, saw that one-third of the caucus votes were cast reflexively against those chairmen with conservative voting records; they recognized that it wouldn't take many more votes to beat them. Suddenly Whitten's AFL- CIO rating shot up 30 points, and he became a strong and effective partisan of the food stamp program. The "boll weevils" of 1981 included almost no Southern Democrats with any seniority, almost no senior members with important committee posts to lose. That's an important reason for the lower defection rate, and it will continue to operate.

* Help out your friends. The speaker worked to make sure that, in the 1982 elections, it would pay to stay with the leadership. He channeled support, for example, to North Carolina Democrats who had stayed loyal on the budget and tax cut votes and were under attack from Jesse Helms's Congressional Club. They all won, and added to their numbers. In contrast, boll weevils did rather poorly. Not only was Ron Mottl -- the one Northern boll weevil -- defeated in his primary in the Cleveland suburbs, but so was Billy Lee Evans in his primary in south Georgia. Phil Gramm, the intellectual leader of the boll weevils, won his primary in rural Texas, but with 62 percent of the vote -- a percentage low enough to suggest trouble for an incumbent. In 1983, perhaps 10 of the 30-odd boll weevils can be expected to come back to the leadership.

Adding the 10 Northeast Republican and 10 boll weevil votes to the 26 seats the Democrats gained in the elections leaves the speaker 40- odd votes stronger than he was last year. It puts his strength well above the 218 vote majority.

But that doesn't mean the speaker is about to introduce vast big-government programs. To understand that, you have to understand where the Democratic votes and 1982 gains come from. Only 59 of the Democrats in the new House will be from the industrial heartland-- the belt from the Appalachians around the Great Lakes and down to Missouri whose economic base seems permanently changed. Only 12 are from the Farm Belt and eight from the Pacific Northwest -- areas hurt, probably only temporarily, by low farm prices and the housing slump. Demands for massive government aid and measures to prop up local economies -- like the UAW's local content bill -- will have limited constituencies. Only 57 House Democrats are from the Northeast, generally the supporter of big government. Almost as many -- 95 -- are from the South as from the Northeast and the industrial heartland put together. Another 28 are from California, which, like the South, has a positive long-term economic outlook. This is not a constituency for big-government programs, and the speaker has shown that he won't try to dragoon Democrats into supporting measures that the large majority of them are not comfortable with.

What will he do? O'Neill's tone on election night was conciliatory, and his capacity for compromise will be tested by the Social Security issue. The commission headed by Alan Greenspan is supposed to meet next week and reach agreement by Dec. 1. Its membership is bipartisan; some -- Rep. Claude Pepper, ex-Social Security Commissioner Robert Ball -- were appointed by O'Neill. The commission can reach agreement only, it seems, by agreeing to cut some future benefits and increase some taxes. The question then is whether Tip O'Neill's House will support such a compromise. It means giving up one of the Democrats' strongest 1982 issues; and the Republicans will not back benefit cuts without the camouflage of bipartisan support. Can he orchestrate the intricate business of assembling a majority for a Social Security bill? It will be a good test of the leadership he's demonstrated and of the mettle of the Democratic majority.