They had a subdued last hurrah on State Street today for Sen. Edward M. Kennedy, the big Irishman from Boston whose Illinois primary campaign ended with little of the joy associated with St. Patricks Day.

Wearing a green sash that proclaimed him a "Son of St. Patrick," Kennedy made a final Illinois campaign appearance in Chicago's annual St. Patrick's Day parade, an event that contained enough negative symbolism to summarize the state of his political fortunes, here as well as nationally.

The weather was hostile as a heavy wet snow, whipped by raw winds off Lake Michigan, swirled around the bareheaded candidate. The crowd was less hostile, as many reached out to shake his hand, but others among the thousands who lined State Street today booed Kennedy with almost as much lusty enthusiasm as they booed their mayor, Jane Byrne.

There is widespread agreement here that Kennedy will be defeated by President Carter, even within Chicago, in Tuesday's Democratic presidential preference primary. A final Chicago Tribune poll published today showed the president had lost six percentage points in the last week, but still held a commanding 56-to-23 lead over Kennedy.

Moreover, while the poll showed Carter slipping, Kennedy's 23 percent share of the electorate was exactly the same as a week ago, further evidence that the Massachusetts senator is not benefitting from any growing disenchantment with the president.

Faced with this gloomy prospect, Kennedy has based his effort here on the hope of converting the support of Byrne and the Cook County Democratic organization into a large share of the 49 convention delegates to be selected in the city.

He stands a chance of doing that, because under Illinois' two-tiered primary system, Democrats will vote twice in the presidential primary. The first vote will be a choice between Carter and Kennedy in the nonbinding preference "beauty contest," in which the president appears to hold an insurmountable lead.

But, in a separate vote, voters also will select 152 convention delegates from thoughout the state. Between five and eight delegates will be elected in each of the state's 24 congressional districts. The delegates are listed separately on the ballot as pledged to Kennedy or Carter, though they are not legally bound to the pledge.

With almost a third of the state's delegates at stake in Chicago, Kennedy's limited hopes rest with the ability of the organization's disciplined precinct captains to deliver the vote for his delegates even if they can't sell him as the candidate in the beauty contest. Kennedy campaign officials concede that the president should win most of the delegates elsewhere in the state.

The Chicago Democratic organization, however, is in disarray, headed by a controversial and increasingly unpopular mayor and in danger of losing some important local elections Tuesday to insurgent challengers.

Byrne has proved a liability for Kennedy in terms of popular support, even turning the St. Patrick's Day parade, an event meant to signify unity when "everyone is Irish" for a day, into a political controversy. Last week she defended her invitation to Kennedy to march in the parade, explaining that "he's Irish and Irishmen should be in the parade."

What about the president? She was asked. "He's English," the mayor snapped.It was into this atmosphere that Kennedy stepped this afternoon to take his place with Byrne at the head of the parade as it formed at the corner of State and Lake streets.

Byrne, dressed in a fur coat and a green workman's hat, led the way south on State Street. She waved to the crowd, but her face was set in a hard frown at the sound of the boos and occasional shouted obscenities.

Kennedy quickly and symbolically began putting distance between himself and his most prominent Illinois supporter. In an atmosphere that soon turned to chaos, he and an accompanying mob of reporters, cameramen, police and Secret Service agents began swinging from one side of the street to the other so that the senator could shake hands with the crowd.

As security agents shoved the reporters and cameramen to the side and up the street, Kennedy's obviously terrified wife, Joan, clung to her husband's side, clutching his shoulder as she was dragged along.

The handshaking slowed Kennedy's progress and he fell further behind Byrne. At the corner of State and Madison, his name was announced on a public address system and the booing was clearly audible.

Byrne had passed the same spot moments earlier and was greeted by a stronger chorus of boos.

Byrne has boasted publicly that she will deliver all 49 of Chicago's convention delegates to Kennedy. Carter aides here, however, are privately confident that they can pick off some of the Chicago delegates and are prepared to claim any inroads in the city as a major victory for the president. p

Reflecting their optimism over the Illinois results, Carter campaign aides today began pointing at their accumulation of delegates around the country. Tim Kraft, Carter's national campaign manager, said the campaign staff's projection of delegate strength showed that even in a "worst-case scenario" in which Kennedy won such major primaries as New York next week and California and Ohio June 3, the president still would win the nomination.

But Kennedy has vowed not to let Illinois be the literal last hurrah of his campaign and to stay in the race to the August convention. His Illinois campaign coordinator, Paul Tully, said today that for all its internal turmoil, the Chicago Democratic organization remains a powerful force that could salvage a respectable number of delegates for Kennedy.