About a month ago, recalls Rep. Mary Rose Oakar (D-Ohio), President Reagan told a "welfare story" at a meeting with congressional leaders. It was about a jobless welfare recipient who phoned the employment service ostensibly to look for work, but who hung up immediately when told it was available.

Oakar, who attends the White House meetings as secretary of the House Democratic Caucus, says she and other Democrats who were there -- led by the Speaker of the House -- were "livid."

"So I raised my hand and the president said, 'Yes, Mary Rose?' I said, 'A lot of unemployed people are very proud and don't want welfare. I know 50-year-old unemployed workers who will not take welfare. It's not true that people prefer welfare.' "

The incident illustrates a lot about Oakar and why she is receiving increasing attention as a tough legislator squarely within the liberal Democratic social welfare tradition.

"She speaks up, that's for sure," said a Republican who asked not to be named. "She stands by her guns and doesn't hesitate to let you know what she's thinking -- and she knows what she's talking about," said a Democratic official.

The perception is also beginning to spread that Oakar, 46, a 10-year veteran of the House, is a strong party activist of remarkable energy. She is unusual in serving on four committees: Banking, Aging, Post Office and Civil Service, and House Administration. At the Select Committee on Aging, she heads the task force on Social Security, elderly and women. She also chairs the key Post Office and Civil Service compensation and benefits subcommittee, which handles federal employe pensions, health benefits and pay.

And in recent years, Oakar has risen within her party. A member of the Democratic National Committee, she serves as House congressional liaison to the DNC and as an at-large House Democratic whip. She is starting a political action committee called Economic Security PAC to help female candidates, and she speaks at colleges to help recapture the campuses for the Democrats.

"I think the kids are coming around," she says. Oakar calls herself a "moderate" Democrat, but others call her a traditional liberal. She says that when people hear the specifics of what President Reagan wants to cut in domestic programs, they respond well to the Democrats.

Oakar, first elected to the House in 1976, has won most elections since by huge margins; in 1984 she had no opposition and only 44 write-in votes were cast against her. Representing downtown Cleveland and suburbs that include many white ethnic working-class people, she has built a strong pro-labor record.

Increasingly, Oakar also has become associated with women's issues -- pay, pensions and Social Security protection -- and with consumer matters. These issues have been in political decline in recent years, but Oakar persists.

On the other hand, while she supports the Equal Rights Amendment and family planning and has sponsored numerous bills on women's benefits, she recognizes that "certain women's groups will never endorse me" because of her stance on abortion. She opposes Medicaid funding of abortions and favors special benefits for pregnant women to provide alternatives to abortion.

The youngest of five children in a Maronite Catholic family, Oakar was born in Cleveland, attended Roman Catholic schools, got her B.A. in English, speech and drama at Ursuline College in Cleveland and her M.A. in fine arts from nearby John Carroll University. Her father, a Lebanese immigrant, was a steelworker, construction worker and stonecutter.

She once thought of working on the stage, but turned to teaching instead -- for four years at a high school and for six years at Cuyahoga Community College in Cleveland, where she taught English, speech, drama and fine arts. Although she almost was fired for starting a union at the college, she says, "technically I am still on leave from Cuyahoga."

She began her political career as a neighborhood activist, served on the City Council from 1973 to 1976, and made a bid for Congress when the incumbent sought a Senate seat.

When she came to the House, Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) kept calling her "Rosemary." When she mentioned this, he explained that he has a daughter named Rosemary and a sister named Mary Rose, and that he's always had trouble keeping the names straight.

Oakar is philosophical about being a leading woman in a traditionally male club. "I really can't say I have suffered discrimination in the House because of being a woman. At times the fellows go out of their way to not leave you out." But she says women in the House do feel a special bond, "because after all, there are only 24 of us."

Oakar has a heavy agenda in the 99th Congress, with a special emphasis this year on banking legislation. Because many banks "only want to cater to large accounts," she is pressing to require banks to give certain free services, to bar a minimum balance requirement and to pay interest on all balances.

She is concerned about interstate banking takeovers in which big banks buy smaller banks and funnel the money from depositor savings to investments in other areas. With Rep. Charles E. Schumer (D-N.Y.), she wants to introduce legislation requiring large banks to reinvest money in the local community and to make their portfolios public. The Banking Committee has endorsed the idea.

She also has been pushing (so far without success) for big increases in Social Security benefits for women: more free credits for years of absence from the labor force for child care, better benefits for widows and widowers, and above all, for earnings-sharing -- a highly controversial plan to give a person Social Security credits for half the earnings of her or his spouse, thereby entitling these people to Social Security disability or old-age benefits on their own.

She is also a strong advocate of improving private pensions for women -- for example, cutting the 10-year vesting requirement, which works to the disadvantage of women who join the work force late or who take time off for child care, to five years.

An Oakar-engineered House bill calling for a broad study of pay equity for women and minorities in the federal pay system awaits Senate action. "Women are now 40 percent" of the federal labor force, she says, "but they're clustered in the bottom four rungs" of the scale.

Oakar also describes herself as "a big advocate of federal workers. This administration is just trying to take everything away from them -- gut the retirement system, gut their health benefits and gut their pay, too."

While cutting an increasingly high profile in Washington, Oakar still has that other attribute of successful politicians: she's a big home-town booster. Cleveland, she says, is enjoying a "fabulous regrowth" after being hit hard by the shrinkage of heavy industry. Employers based in the city or nearby include TRW, Standard Oil, Eaton, LTV Steel and the only National Aeronautics and Space Administration center "north of the Mason-Dixon line and east of the Mississippi." Cleveland, she says, "is second only to New York in the arts, with the Cleveland Orchestra, all the museums, magnificent old theaters now being revived instead of turned into parking lots, outstanding health institutions."

In fact, Cleveland's health institutions are such that "one year, five members of Congress had heart bypasses at the Cleveland Clinic. I kept sending them baskets of flowers."