"Back Reagan!" Diane Rossie whispered to fence-sitting Rep. Lyle Williams as he entered the Holiday Inn-North here last Friday to face social workers lobbying against President Reagan's budget cuts.

Rossi is a social worker herself, a supervisor in the Mahoning County (Youngstown) welfare department. But she told Williams that many welfare recipients "are loafers who can work if they want to" and the program "is full of waste." A lifelong Democrat, she voted the straight Republican ticket last year.

Once inside the meeting, Rossi was lost among 300 social workers frowning and shaking their heads over Reagan's budget outrages. The contrast symbolized the mood in this economically ravaged former steel city after Reagan's first 100 days. While the city fathers are horrified, there is substantial support for the Republican president from the overwhelming Democratic electorate.

Whether or not Reagan is the cause, there is hope for economic revival in the Mahoning Valley not visible to us on a reporting trip here almost a year ago. Industrialists who had given up hope for Youngstown have changed their minds because of the new spirit. The United Steelworkers Union has agreed on a plan to increase productivity at Commercial Shearing, Inc., plants here that will close unless they show a profit. General Motors management and the United Auto Workers at the notorious Lordstown plant nearby, after years of shouting at each other, sat down Friday to discuss productivity and quality.

This is the backdrop for the difficult decision facing Williams, who in 1978 moved from his barbershop to Washington as this district's first Republican congressman in 42 years. No conservative (42 percent by American Conservative Union ratings), he is disliked by businessmen. No liberal (33 percent by Americans for Democratic Action ratings), he is despised by the social welfare establishment. He won an unexpected re-election landslide in 1980 by coming home from Washington every weekend and by cutting a fine line down the middle.

But there is no middle on the budget. Williams soon must choose on the House floor between the Reagan budget and the Democratic alternative of Rep James Jones. Williams discloses, "I'm interested in the Jones budget," making him one of a handful of Republican House members who might defect on Reagan's first decisive vote.

Williams, who carried this district by 30,000 votes while Reagan was losing it by 7,000 does not want to appear as a regular Republican knucking under to the president. City leaders try to exploit Williams' independence by making ferocious warnings. Pete Stark, senior member of city council, says angered welfare recipients may kill for food. Mayor George Vukovich fears the city will be burned.

Such talk is fanned by the social welfare bureaucracy. The Holiday Inn emergency meeting was attended by paid professionals, men in three-piece suits and women in expensive dresses, with much at stake. Veteran County Commissioner Tom Barrett commented wryly as he entered the jammed meeting room, "It looks like a save-our-jobs-rally by the social workers."

Williams has no intention of saving their jobs. "There is no question that you are going to be cut," he told them Friday. What bothers the congressmam is Reagan's plan to eliminate the Economic Development Administration, credited with the forthcoming construction of a 1,700-job aircraft factory here. Unless Reagan offers a viable economic development alternative, williams says he "absolutely" will vote with the Democrats for the Jones budget.

Yet, Williams has no illusions about EDA, which he says created 13 new jobs at the cost of $6 million in trying to develop an industrial park here. A major change in Youngstown is that hardly anyone believes any longer that either the rusting steel mills will reopen or that the federal government will provide money for new industries. "This town is going to have to do it itself," contends Democratic City Councilman Roland Fabrizio.

There is help from Reagan's Washington, but in money, as shown when bureaucrats at the Environmental Protection Agency started tangling up a modest Republic Steel Co. construction plan in Youngstown. Williams placed a call to the White House, the White House called EPA and the tangling ceased.

That incident helped build pro-Reagan sentiment after 100 days, including praise from the heart of the Democratic leadership. "The people like Reagan," says highly respected Democratic State Rep. Tom Carney. "I admit I like him. There's a lot in his program that makes sense." Mahoning County's outspoken Democratic Chairman Don Hanni says, "I think people like the idea of cutting taxes." GM assembly line workers also like welfare cutbacks, according to UAW leaders.

The mood of the 85 percent or more of workers here who are employed was expressed by Williams when he told the social workers that "the work force out there" can no longer support their activities. "We cannot let it get to the point," he added, "that they [the workers] do not have any incentive to keep going." One person in the rear (was it Diane Rossi?) applauded. But the views of workers will be weighed more heavily than those of social workers as Lyle Williams ponders his budget decision.