Washington — If Howard Henry Baker Jr. is sad or sentimental about the closing days of his career in the United States Senate, he's certainly not showing it. In the midst of recent parliamentary chaos as the Senate struggled to wind up its work for the year, the majority leader took the floor and vowed that no one ''in this galaxy,'' or, in fact, in any galaxy yet sighted, wanted Congress to adjourn more than he. He spoke with good-humored exasperation, which has been his patented style of leadership in the unruly Senate.
After 18 years in Congress, the genial but intensely private Tennessean is walking away from his post as the first Republican majority leader of the Senate in a quarter-century. And if he does not miss it, the institution he is leaving will almost certainly miss him.
In his brief four years as majority leader, Senator Baker transformed the Republicans from their minority role as critics into a majority responsible for making the policies of the land. He was the President's man on Capitol Hill, where he ushered the historic Reagan program into law in 1981. Far from incurring hostility, he became known as the Senate's great conciliator.
Even the majority leader he displaced, Sen. Robert C. Byrd (D) of West Virginia, normally guarded in his words, lavishes praise on Baker. ''He is well liked by everyone on both sides of the aisle,'' says minority leader Byrd, speaking of his ''tremendous respect'' for Baker and of a ''friendship that will last forever.''
Sen. Strom Thurmond of South Carolina, goes further. In Mr. Thurmond's 27 years in the Senate, he says, ''I don't think we've had a finer majority leader. I think he's been able to accomplish a great deal that LBJ (one-time majority leader Lyndon B. Johnson) had to do through domination.''
Less-partisan observers also give Baker high ratings. ''I think he'll rank high'' among Senate leaders, says Thomas E. Mann, executive director of the American Political Science Association and a close observer of Congress. But he adds of Baker's four-year tenure, ''It's probably a little short for a leader to leave a major mark.''
His most lasting accomplishment will probably be passage of the Reagan tax cuts and budget-reduction packages in rapid fashion in the first few months of the then new administration. Ironically, Baker, who challenged Ronald Reagan for the presidential nomination in 1980, gave the President the most wholehearted support of any majority leader in recent memory.
''He's been a lion in support of the cause which unites us,'' Reagan told a Howard Baker ''roast'' last month.
If there is any carping about the Baker leadership, it has centered on that loyalty. Most Republicans applaud it, but some have complained privately that he has not been independent enough of the White House.
''If (a bill) was what the President wanted, he did his best to see that it was brought to the floor,'' says Sen. Nancy L. Kassebaum (R) of Kansas, applauding Baker's ''legacy'' of supporting the President's programs, even when it meant setting aside his own preferences. But she says that some of her colleagues ''felt the Senate view wasn't forcefully expressed'' in dealings with Reagan.
Such has not always been the case for congressional leaders. Senator Byrd recalls that when President Carter took office, ''I stated I was a Senate man, and I would take always into consideration my party members.''
Some Republicans are said to be hoping their next leader will lean more toward the Byrd approach, but Baker's style is in keeping with his view of government.
''The antagonism that has grown up between the legislative and executive branches is among the least healthy aspects of government in our time,'' Baker wrote in an essay published last spring in the New York Times.
The Baker move to shorten senatorial sessions also fits into the Tennessean's political outlook. Since his early senatorial campaigns, he has advocated reducing the government. Complaints about being imprisoned in the nation's capital is a favorite theme.
On a visit to the Tri-Cities area of Tennessee before he announced his retirement, Baker told a chamber of commerce gathering ''how good it is to be out of Washington,'' then proceeded to tell a joke about two tourists at the US Capitol who heard the bells ringing to indicate a vote on the floor. When one asked what the bells meant, Baker said, the other visitor responded, ''I don't know. Maybe one of them escaped?''
His ideal, as he has described many times on the Senate floor, is a citizen legislature that would bring lawmakers to Washington part-time, just as Howard H. Baker Sr. did as a congressman from Tennessee.
Baker had no more success at realizing that dream than in passing his pet proposal, televising the Senate chamber. The failure is not a sign that his low-key leadership was ineffective, says Senator Thurmond. ''I don't know that anyone could have gotten that through.''
Nor did Baker, one of the masters at snaring federal projects for his state, have enough clout to save the much-discredited multibillion-dollar Clinch River nuclear breeder reactor for Tennessee.
Moreover, after the Republican senators marched to the Reagan beat for the first 18 months, they began to break ranks by 1982, straining Baker's consensus-style leadership. At times, especially at the end of sessions such as this week, order in the Senate collapsed, sparking complaints that perhaps Baker is too nice.
Baker has made it clear that he isn't leaving politics when he leaves Congress in January. ''He never intended to do this (stay in the Senate) the rest of his life,'' says Baker's closest aide, Tom C. Griscom.
His first order of business, Baker's associates say, is to rectify his financial situation, despite the fact that he is far from poor. He and his wife , Joy, the daughter of the late Republican Senate leader Everett M. Dirksen of Illinois, have assets of well over $1 million. Baker will add considerably to that when he joins a Washington law office at a salary reported to be $700,000 or more.
Baker has also made little secret of his desire to make another try at the presidency, even if his first was a failure. He has collected more than $1 million for his Republican Majority Fund, earmarked for financing his travels to speak for congressional candidates. The travels will give him national exposure before the 1988 elections.
Will civilian Baker be a contender for the White House? ''I don't have any feel for that at all,'' says Sen. Richard G. Lugar (R) of Indiana, who ran Baker's first presidential campaign. But Senator Lugar points out that Walter F. Mondale spent four years as a private citizen before winning the nomination.
The moderate Baker has yet to spark much voter interest. His tough anti-Mondale speech at the conservative gathering at the National Republican Convention in Dallas last summer was a bust. ''He's uncomfortable giving attack-type speeches,'' says Ronald D. McMahan, editor of the Knoxville Journal and former assistant to Baker. He notes that Baker is not easily discouraged: He lost his first race for the Senate and tried three times before being elected GOP minority leader in 1977.
Mr. Griscom concedes that there are obstacles to the presidency. Baker will need ''a niche, a message,'' he says, and he will also need to court conservatives, who have ranged from hostile to indifferent.
For now, the retiring majority leader must settle for the likes of a high-powered job in the capital, a political travel fund to keep himself before the public, his photography hobby, and regular visits to his 10-acre estate in the mountain hamlet of Huntsville, Tenn.