Picture, Campaigning for her brother-in-law, Sen. Edward Kennedy, in Sunday's Democratic primary in Puerto Rico, Jacqueline Kennedy Onassis greets voters. AP

Sen. Edward M. Kennedy's fragile hope of making a credible showing in next Tuesday's Illinois primary rests with people like Adella Weiss.

She is in her 60s, a truck driver's widow living on a pension, and, while not finally decided, she is inclined to vote for Kennedy. Standing at the front door of her modest frame home in Evergreen Park, an older suburb that borders Chicago's southwest side, she spoke the other night about President Carter.

"As far as the hostages are concerned, I'll stick with him," she said. "But on the other things, I don't -- the prices, the cost of gas."

With the inflation rate near 20 percent, Weiss is the kind of voter Kennedy has targeted in his campaign here. Emphasizing the nation's economic woes, Kennedy says his calls for wage and price controls and an across-the-board economic freeze are the only answer to inflation.

But when the Massachusetts Democrat arrived here tonight for three days of campaigning, public opinion polls and campaign officials on both sides of the Democratic presidential race suggested that the growing concern over the economy is coming too late to do him much good here.

For every voter like Weiss, there appear to be considerably more like her neighbor, Debbie Edgin, a young housewife and mother of three children who dismisses Kennedy as "just running or his name," on Jerry Broadhurst, 42, manager of a life insurance agency who is disgusted by "too much government spending" and will stick with Carter.

A Chicago Tribune poll published earlier this week backs up the assessments of officials in both campaigns that the economic issues Kennedy is stressing are beginning to have an impact, but not enough for him to over-come his other problems and pull even with the president.

The poll, conducted last weekend while Kennedy was campaigning in the state, showed Carter holding a 62-to-23-percent lead. This was down slightly from earlier polls, but the margin was wide enough to reassure Carter campaign aides who admit to nervousness over how inflation, the continuing stalemate in Iran and the administration's blunder in the United Nations vote censuring Israel are affecting the president.

Neither side expects the final margin to be that wide as Kennedy struggles for a respectable showing here in the popular vote "beauty contest" part of the primary. But with Kennedy campaign aides unwilling to predict that the senator will win a majority of votes in any of the state's 24 congressional districts, the real contest is over the 152 convention delegates who will also be selected in the primary.

Under Illinois' two-tier primary system, voters in each congressional district will vote their presidential preference between Carter and Kennedy and separately vote for between five to eight convention delegates pledged to one candidate or the other.

Here Kennedy's chances appear much better, principally because of the backing of the Cook County Democratic organization and Chicago Mayor Jane Byrne, who has publicly pledged to deliver all of the city's 49 delegates to Kennedy.

But even in working-class, organization strongholds where the economy is the overriding issue, Kennedy's popularity appears to be lagging. In some areas, in fact, Democratic ward leaders are handing out sample ballots with the names of Kennedy delegates checked off but which show no preference in the beauty contest portion of the primary.

"If he's losing 3 to 1 and you're fighting for local candidates, you just don't need another fight," one ward leader explained.

Larry Hansen, the Carter campaign's Illinois coordinator, believes that a number of factors account for Kennedy's failure to make more headway against the president on economic issues.

"I've determined that the public does not trust any politician who comes up with a quick fix, whether it's wage and price controls or something else," he said. "The problem is so big that people realize no president can solve it. Add to that the view of Kennedy as a profligate spender and what it all adds up to is a very large measure of tolerance of Carter."

But Hansen is nervous enough about the impact of inflation to have suggested to Washington-based Carter aides that the president would do himself no harm if he announces his new anti-inflation measures before Tuesday.

Paul Tully, a Kennedy organizer in the state, also blames the so-called "character issue" that has plagued the Kennedy campaign from the beginning for blunting the senator's economic message.

"There is more of a Chappaquiddick factor in this state than we've run into in other states," particularly among Chicago's concentration of ethnic Catholics, he said.

To try to offset that, Kennedy's wife, Joan, was in Chicago earlier this week, making the rounds of local television studios where she answered a series of excruciatingly personal questions about her husband's lifestyle.

For both Carter and Kennedy, the outcome in Illinois and in the New York primary a week later may revolve in large part around questions of time -- for example, how long public tolerance of high inflation will continue, and how long Kennedy can keep his sagging campaign afloat without a victory outside his home state of Massachusetts.