If you ask Rep. Jack Brooks (D-Tex.) about himself, he draws a picture of a Gulf Coast Henry Higgins - "Just an ordinary man . . . who wants to live his life free of strife . . ."

The feisty chairman of the House Government Operations Committee has made himself President Carter's chief antagonist on the issue of government reorganization, precipitating a battle that has punctured prematurely all talk of a Capitol Hill honeymoon for the new President.

But the 54-year-old Beaumont, Tex., bantam just can't understand why people think of him as cantankerous and combative.

"I think of myself as someone who tries to be constructive," he says, "someone who understands that politics is the art of compromise, that it's a lot more important to get something done than get into a lot of battles and get a lot of publicity. All you do is make enemies that way, and who wants to have enemies?"

Brooks leans back in his chair in the Rayburn House Office Building suite, a beatific smile surrounding the cigar, his blue eyes as guileless as a child's.

Yet the speaker of these words is the same Jack Brooks who has faced down Jimmy Carter in several head-to-head meetings, who is described by a former aide to Lyndon B. Johnson as "one of the few men LBJ was ever afraid of," a man that Richard M. Nixon once called "the executioner" in the House Judiciary Committee's impeachment hearings.

The man who will preside at House committee hearings on Carter's cherished reorganization plans is the same Jack Brooks whose warmth has been felt by uncounted numbers of military contractors, manufacturers, bureaucrats, politicians, colleagues and Presidents, a man whose withering scorn and sarcasm are burned into the hides of witnesses such as Arthur Sampson.

Sampson was the head of the General Services Administration in 1973 when Brooks' subcommittee began looking into the government's expenditures on President Nixon's San Clemente and Key Biscayne homes.

Hard-pressed to defend the $10 million invested in the properties, Sampson said at one point that the added facilities actually had reduced the homes' market value.

"Oh, really," said Brooks, in his best country-boy manner. "Well, Mr. Sampson, I'd like you to come down to my farm and desecrate it a little bit."

Ask a dozen people - House colleagues Texas politicians, Washington lobbyists, officials of past administrations - about Jack Brooks and the words you hear most often are: tough, smart, partisan, prideful and driven. "He's got more damn complexes that the law allows," says one Texan who has known him for more than 30 years.

But ask those same people the question Carter's White House aides are asking - "What does Brooks really want?" - and you get a surprising answer. Or non-answer.

"Jack Brooks isn't after anything," says Robert S. Strauss, the former Democratic national chairman, one of several people who have tried, without success, to mediate the disagreement between the President and the Government Operations Committee chairman.

"He's sincere in his position, and he knows the President is sincere in his, and they've just agreed to disagree," Strauss says.

Carter says he wants the same reorganization powers Congress granted to every President from Harry S. Truman to Nixon. Under the authority, a President could reshuffle subcabinet agencies by submitting reorganization plans to Congress that take effect automatically unless vetoed by the House or the Senate within 60 says.

Brooks, who opposed extension of those powers in 1971, says they should not be restored to any President, even a Democrat for whom he campaigned.

Instead, he is offering a counterproposal that would allow a reorganization plan to take effect only when affirmatively approved by both houses of Congress. The bill would prevent any plan being held in committee of more than 45 days, but Carter has rejected it as too cumbersome a method for reorganization.

"I have nothing against Jimmy Carter," Brooks says. "I campaigned my district for him and we gave him 30,000 of his 150,000 vote margin in the whole state. I want him to be a good President and I want to see reorganization go forward. But this is just a matter of principle to me. It's a very bad and dangerous delegation of authority to a President."

"People don't recall, Brooks said, "that one of the first plans Nixon submitted was the reorganization of the White House staff to create the Domestic Council. That concentration of power permitted him to commit most of the abuses for which he was later found guilty."

Brooks' enmity for Nixon was so well-advertised by both men that many in Washington consider Brooks a chronic presidential antagonist. But the record indicates otherwise.

When Brooks came to the House in the election of 1952, he developed what he calls a "friendly, responsive relationship" with the fellow-Texan in the White House, Dwight D. Eisenhower.

He had a "good solid, close relationship" with President Kennedy and was a Johnson intimate. Despite the fact that they were sometimes at odds on patronage matters. Brooks was a frequent White House guest, visiting often in the family quarters and using the President's bowling lanes even when Johnson was elsewhere.

"I think he wants that kind of status and entree again," said one veteran of the Johnson years. "It's more psychological between him and Carter than it is political. I think if Carter would flatter him publicly and send Amy over to play with his kids, this problem would be solved."

Others are not so sure. They see Brooks as a man who "loves a fight, and the bigger the opponent, the better."

"He's an instinctive loner," says a colleague. "He's got a helluva chip on his shoulder," says one man who tried to deal with him for the Nixon White House.

The stories of his feuds are legend, and one of the most serious, many of his colleagues believe, is with his fellow-Texan, Rep. Jim Wright of Fort Worth, now the House majority leader.

A former Texas newsman recalls that Brooks and Wright came to the Texas legislature as freshmen in 1947. "Jim was this good-looking, charismatic guy, out-front the start. And Jack was the wizened little fellow from the wrong side of the tracks in Beaumont, just sitting in the back row, eyeing him. You've had the Jim and Jack competition for 30 years."

Brooks, predictably, scoffs at the notion. "We're not rivals at all," he says. He's never run for anything I wanted and vice versa. We're friends."

Yet Brooks was one of two Texas Democrats who failed to endorse Wright for majority leader. The reason, he says, was that he had given a commitment to Rep. Philip Burton (D-Calif.) before Wright entered the race.

If Brooks's enmities are enduring, so are his friendships. He and Texas Gov. Dolph Briscoe, a Democrat, became friends at the University of Texas. Brooks, who had worked his way through high school and college as a part-time reporter and served with the Marine in the Pacific campaign, was an odd partner for the quiet Briscoe, who is as rigidly proper and humorless as Brooks is funny and profane.

But each was best man at the other's wedding, and the friendship has ripened over the years to the point that some ascribe Brooks' current attitude towards Carter to his resentment of the President's treatment of Briscoe.

The Texas governor worked hard for Carter's victory and, many Texans feel, has not received much recognition since Election Day. "It does seem there hasn't been much yet," Brooks observed mildly the other day, "but the administration is new and I'm sure they will show their appreciation for the tremendous job he did."

Brooks insists he is not holding up Carter for appointment of a friend or help for his district. Two former White House lobbyists said that Brooks "never asked the slightest favor," one of them adding: "There were times I wished we could have got a handle on him. But we never found anyone who could influence him, either in Congress or his district."

Brooks has achieved a substantial measure of financial and political independence. He is chairman of the board of a bank holding company and, after winning with 61 per cent of the vote in 1974, had no opposition last year.

His Gulf Coast district has acquired the largest fresh-water dam and reservoir in Texas, extensive Army Corps of Engineers ship-channel construction and other federal largesse. But Brooks is not known as a "hands-out" Congressman, ready to bargain his legislative help for federal pork.

What he is known as is a congressman who waited a long time to achieve a position of power and is acutely conscious of its prerogatives.

With the help of fellow-Texan Sam Rayburn, then Speaker of the House, Brooks became a subcommittee chairman at the start of his second term, when he was 33 years old. But he has endured a long wait for the chairmanships of his two main committees, Judiciary and Government Operations, to turn over.

After 22 years on Judiciary, he is still second in line behind Chairman Peter W. Rodino Jr. (D-N.J.). On Government Operations, the wait was even more painful. The late Rep. William L. Dawson of Chicago became chairman in 1955 at the age of 69 and remained until he was 81. The Rep. Chet Holifield of California took over and held the chairmanship until January, 1975, when he was 71.

A Texas friend recalls kidding Brooks a few years ago about "giving the chairman a gold watch and shoving him out."

"He didn't think it was funny," the friend says.

But if Brooks was impatient, he was not idle. His investigating subcommittee probed everything from the life of light bulbs to the misconduct of airline pilots and the number of coats of paint contractors were putting on government buildings. His investigations saved taxpayers "billions of dollars," the General Accounting Office says, and gave uncounted headaches to his witnesses.

"I've conducted a lot of hearings," Brooks says, "and I've been tested. I never thought being a congressman was supposed to be an easy job, and it doesn't bother me to be in a fight."

Skeptics note that Brooks was in a major fight with President Ford in the last Congress - and lost.The issue was the renewal of the federal revenue-sharing program, which Brooks described, in a typical burst of rhetoric, as "a little monster" and "a snake that should be killed."

Brooks fought the bill and delayed it, but in the end it cleared his committee, 39 to 3, and was paused easily on the floor.

When the White House lined up 24 of the 43 Government Operations Committee members as sponsors of Carter's reorganization authority bill last week, some predicted the revenue-sharing script would be repeated, with Brooks again the loser.

But there is an important difference. Revenue-sharing had to pass Brooks' committee only once every four years. The reorganization authority bill is the first step in a complex process, every part of which is under the jurisdiction of Brooks' committee.

"Carter's going to be dealing with Jack Brooks so often the next four years he's going to see him in his dreams," said one House member. "And Jack is a guy who doesn't forget. If they beat him on this one, they'll pay for it. Oh will they pay for it."

A former White House congressional liaison perhaps put it best. "If Jimmy Carter tries to roll over Jack Brooks," he said, "He'd better get him an armored division. That is one tough guy to take on."

Research assistance on this article was provided by Susan Morrison.