Washington — News of an economic upturn may be welcomed in all quarters, but it has a special meaning for Sen. Richard G. Lugar of Indiana. He has the daunting task of keeping Republicans in the Senate majority. As chairman of the National Republican Senatorial Campaign Committee, he has to defend 19 GOP seats in the 1984 elections. And until recently the outlook looked as bleak as the economy.
Sitting in his office on a cushioned rocking chair, which just arrived from his Hoosier state, Senator Lugar recalls a press report several months ago, when the recession still had a firm grip. ''Almost every single Republican was in jeopardy,'' he says.
''And now most people revisiting the same territory three or four months later would acknowledge that most Republican incumbents appear to have a reasonably good lead,'' says the second-term senator. He concedes that incumbents should be far ahead this early, ''but we are still leading pretty well.''
Lugar, a conservative who is friendly with the Reagan White House, wrested the campaign job last January from fellow Republican Sen. Bob Packwood, a moderate from Oregon whose relations with Mr. Reagan were strained, if not bitter. Senator Packwood had charged that Republicans under Reagan leadership were building a party of white males over age 45.
The far less controversial Lugar has moved efficiently to crank up the campaign committee for the elections. When his colleagues elected him to head the committee six months ago, it was $3.3 million in the red, partly because of a Packwood-Reagan tiff that resulted in Reagan's canceling a fund-raising letter.
Since January, the GOP Senate campaign has raised a net $9 million, more than it has raised in any other entire year. After paying off its debts, the committee has salted away $4 million for next year's senate races.
At the same time, Lugar is working closely with other Republican officials, including those with White House ties.
But Republicans hold that the change in personalities has not been the deciding factor in fund-raising success. ''Principally it is because this is the first election cycle in which it is known in advance that control of the Senate is at stake,'' says Mitchell Daniels, staff director of the campaign committee and longtime Lugar aide.
When the GOP took over the Senate in the 1980 elections, it was a surprise victory. This time Republican contributors have an ''investment'' to protect, he says.
But fund raising has long been the GOP strong suit. Lugar concedes that his party has problems with minorities and with women.
''I think that the Republican Party does need stronger support in the black community,'' he says. He complains that black leaders concentrate on ''simply defeating Republicans'' so that ''everybody has been tarred and feathered in the same fashion'' whether the candidate has a strong civil rights record or not.
He says that his party is ''eager to find out the way and means'' of winning black supporters, but he maps out no strategy. He has hopes that an improved economy will bring some on board and plans to bring black leaders into senate campaign organizations.
Lugar sees the loss of women's vote as a bigger problem for the President than for GOP senators. Senatorial polls show most Republican incumbents have about the same support among men and women, he says.
His strategy for dealing with a possible desertion of women voters is to find more women candidates. ''I'm very, very enthusiastic about the possibility of recruiting women candidates for the Senate,'' he says. Asked if that would draw women back to the Republican Party, Lugar answers, ''It will in the national sense, if there is a perception about Republican enthusiasm about having women as leaders.''
His campaign committee director also stresses the search for women candidates , although he could offer no names yet. ''They are the salvation of the Republican Party,'' says Mr. Daniels. ''I think that a woman Republican is a very potent political package right now.''
As a woman, she is ''immune to the party caricature'' of Republicans, which Daniels describes as a bomb-throwing, inhumane, anti-woman image. At the same time, the woman candidate, as a Republican, ''is reassuring to many of the people who want the country to be defended and the currency to be sound,'' he says.
Lugar predicts that if the economic recovery lasts, his party will hold on to the Senate. He also says Reagan will win reelection, and declines even to discuss the possibility of his not running in 1984.
Lugar also refuses to discuss prospects of stepping into the job of Senate majority leader when Howard H. Baker Jr. of Tennessee steps down next year. Lugar is named on the list of possible successors, despite his relative junior status as a second-term member.
For now he is concentrating on his current job. ''Unless we have a Republican majority, there is not the option to elect a majority leader,'' Lugar says.
But one of his best friends and allies, fellow Indiana Sen. Dan Quayle, a Republican, makes no secret of his preference. ''He's got an ability to get people together,'' says Senator Quayle, adding that Lugar would be acceptable to both conservative and moderate wings of the party.
Lugar, an Eagle Scout and former Rhodes scholar, has earned a squeaky-clean image. His only temporary misfortune was to have been known as ''Nixon's favorite mayor'' when he was mayor of Indianapolis. But he shed that handicap and won a Senate seat in 1976.
In the Senate he is ''not the back-slapping type,'' say his aides. He rarely speaks out on an issue until he has read carefully about it. He tends to answer questions in long, detailed paragraphs.
''Before he starts speaking, you know he's thought it through thoroughly,'' says a top Senate Republican aide.
That is true even in his favorite pastime, running and physical fitness. Before he took it up, he ''read everything there is'' on exercise and physiology , Daniels says. ''He does it by the book.''
True to his conservative colors, Lugar regularly votes against abortion and busing for school desegregation, and opposes ''affirmative action'' plans to promote hiring of minorities.
Unlike some conservatives, he holds that government can come to the rescue when needed.
He helped draw up the legislation to bail out the Chrysler Corporation and New York City. But he added a decidedly conservative touch to those bail-outs, making the medicine just bitter enough that other companies and cities have not lined up for similar handouts.