The hopelessness of efforts to deprive President Carter of renomination can be appreciated by tracing the course of the Illinois delegation in general and state Treasury Jerry Cosentino in particular during the 10 days before the Democratic National Convention in New York.

The possibility that Cosentino, a state Carter-for-Presient leader and delegation co-chairman, might provoke substantial numbers of Carter delegates into rebellion excited Sen. Edward Kennedy's campaign and alarmed the White House. That rebellion was aborted by a combination of the Carter campaign's diligence (utilizing the first lady and the vice president) and the inflexibility of the "reformed" nominating process.

So there will be few defectors among Carter's 163 (out of 179) Illinois delegates Monday night at Madison Square Garden when they vote on the rule to bind themselves to last March's primary outcome. Cosentino will go along with the president, though he fears the worst Nov. 4 against Ronald Reagan. Here is Illinois loyalty that nails down Carter's renomination.

That was not certain as the Billy Carter affair came to dominate the headlines. Illinois seemed shaky. Not only did the president have more delegates from here than any other state because of his March primary landslide, but most were "Carter worshippers" (the contemptuous description by a pro-Carter professional). Thus, any major Illinois defection would be leveraged across the country.

That's why Cosentino, one of the few practicing politicians on the delegation, quickly got the Carter camp's attention when he commented that he as president would not press for a binding rule. It seemed possible that he might vote against Carter on the rules fight. Would that presage Illinois defections on the nomination itself?

Apart from the rules fight's merits, Cosentino reflected the mood among Democratic politicians here and elsewhere: pessimism about November, skepticism about Carter's general election campaign strategy. Cosentino insists the president cannot carry Illinois until he makes peace with Chicago's pro-Kennedy Mayor Jane Byrne, but feels the advice goes unheeded. "There is no input to these people," Cosentino told us.

His gloom is common among the state's Democratic politicians. Secretary of State Alan Dixon, who once viewed an easy road to the U.S. Senate this year but now is threatened by a Reagan landslide, has called for an open convention. Dixon is signaling than he wants neither to displease Mayor Byrne nor pick up an unwanted Carter label.

Dixon, like most Illinois office-holders, is not a delegate. Only a quarter of the delegation has any previous identity in politics, and scarcely 5 percent of those could be called "regular." Consequently, when Carter operatives here reported some 25 defectors on the rules fight with a possibility of a great deal more than that, Mayday sounded at the White House.

Cosentino, a 49-year-old ex-truck-driver and self-made businessman, was summoned to Washington for two days of hand-holding. He conferred privately with Vice Presient Walter F. Mondale and campaign Chairman Robert S. Strauss and was taken out for a high-priced dinner.

Carter's telephone brigade targeted the Illinois delegates wavering on the rules fight. Bud Loftus, as well-known Democrat from suburban DuPage County, was telephoned by Rosalynn Carter herself. Tony Scariano, a veteran liberal from Chicago Heights, received uninterrupted telephone promptings, from Mondale on down.

This campaign, coupled with the solid pro-Carter front at the governors conference in Denver and the president's effective televised explanation of the Billy affiar, calmed the rebellion. Cosentino climbed back on board. Loftus is now undecided. Scariano still opposes the binding rule (while vowing to support Carter in any event), but he is now among a diminishing number of rules rebels -- perhaps less than 15. That's not enough to make a stir.

The rebellion collapsed so quickly in part because no viable alternative was sighted. Cosentino calls himself a "moderate-to-conservative" and abhors Kennedy as "the biggest liar in politics. "But he has no love for the Democratic right's longtime champion, Sen. Henry Jackson; when Jackson upbraided the Carter record at a party fundraiser in Chicago this year, Cosentino snorted, "This is ridiculous," and walked out.

He contends Democrats had better stick with Carter, like it or not -- reflecting fatalism and frustration among Illinois Democratic politicians identical to the attitude of the governors in Denver. The politicians here think the president will be sandbagged by Byrne in Chicago, could be devastated by Reagan in the suburban "collar" counties surrounding Chicago and is dead among the downstate farmers. But they are stuck with him, will back him in New York and then hope for a Trumanesque miracle.