Jerry Brown broke out of the starting gate first - bolting to the steps of the Executive Office Building to be embraced by the press while President Carter was saying goodbye to the governors.

Once again - as he had all during the three-day National Governors' Conference annual winter meet - Brown had beaten everyone at the one game in town, publicity.

Most of the other governors were trying, with varying degrees of success, to perfect the low-key technique of seeming indifference; while still being "available." One such was Illinois' Gov. James Thompson. "He was not going to get into a foot race with Brown," commented an aide.

At 6 feet 6, he is not easily hidden. And as the Republician Party's current biggest success story - he won by a record margin of 1,390,000 votes over a Mayor Daley-picked candidate - Great Mention. Quickly touted as a possible 1980 presidential nominee, Thompson has done little to disabuse anyone of the is a goal he's thought of "since I was 11.

And so last year, qith that head of steam, Thompson rolled into the conference in a blue turtleneck, plaid shirt and sport coat. His colleagues were in gray. Thompson, the new comer, said there were npapprentice-ships in this game of politis any more, then proceeded to be the strongest to blast the notion that John Connally become Republican National Committee chairman.

This year it was different Thompson was three-piece blue, button-up politics; he talked like the lawyer and professor he was before he became governors. At this time of economic worries, Thompson has apparently figured his present and future constituents don't want charisma, they want an accountant. But an accountant smarter than Jerry Ford. The one achievement he points to in his first year of office is balancing the budget.

Talking small and offering less mean never having to say you're sorry when campign promises are resurrected.

Thompson , at 41 is sandy-haired, thin-lipped and has an easy-going manner. He collects antiques and antuque jewelry; sports two rings. He is earnest as he buries his listeners in facts and statistics about issues that concern him - unemployment, federal relief for the states, passage of the energy bill.

On occasion, he drops the legalese for a one-of-the boys routine. He thought his favorite author of spy novels would ahve created more fiction "while he was in the slammer." Thompson was referring to Howard hunt. At a morining breakfast he greeted millionaire Sen. Charles Percy (R-III) with a slap on Percy's pockets. "just checking for the silverware," He cracked. Percy, taken aback for a minutes, then realized Thompson was referring to Percy's recent stay in the governor's mansion while Thompson was out of town.Then Percy said, "I wouldn't take that cheap plastic they used on us." Thompson laughed heartilty.

In smaller clusters than Brown, Thompson worked the press constantly - impromptu conferences, a U.S. News and World Report lunch, radio shows after a breakfast with Illinois Sen. Percy and Adlai Stevenson III and a gaggle of congressmen, yet another conference in the bar at the Hyatt Regency.

There Thompson took off his coat munched potato chips and sipped Jack Daniels and talk mostly about 1980. A reporter citing the fact that Thompson was in Washington four times within the month, asked if he was not sowing the seeds for a national campaign. He governs the largest Republican run state in the nation, Thompson reminds - a point not lost on Washington. He comes here because he gets asked, he said. "In the coal crisis, if you get called in by the president, what the hell would it look like if l didn't show up?"

his national publicity is "positive - so long as it doesn't appear to the people of Illinois as though I'm trying to exploit it."

There is no name-calling. Ronald Reagan is a certain nemesis but Thompson says only that "it is too soon to tell" about Reagan for 1980.

"It is tooo soon to tell," about Carter. He does not jump on the one-term president bandwagon. After all, says an aside. Carter Is the president of the people of Illinois.

Thompson see more and more a blurring of distinctions between parties. He had thousands of "I Am a Democrat But . . ." buttons made out for the Democrats who followed him in the 1976 election.

Thompson aims for that moderate center of broadest appeal, but at times he gets labeled a conservative (he signed the death penalty bill because it is the "will of the people of Illinois") and a liberal (he vetoed a bill tht would prohibit state Medicaid abortions and another to legalize laetrile - both were overidden.

Thompson won in part because he built up a reputation as a tough United States attorney - indicting more than 350 public officals, policemen, Daley cronies and some Republicans in Illinois. But now he bills himself as a politician. He is proud of the fact that he got along for the most part with the Illinois legislature this year.

While other milled around at black-tie dinners and receptions Monday, Thompson has a strategy session with the Washington-based ad agency Bailey, Deardourff & Eyre, which handled his polished media campaign in 1976. (Thompson has an odd-ball "transition" term of only two years and must run again this year because the state is changing its gubernatorial election years so they no longer will coincide with presidential elections.)

Yesterday morning at 8 he praised the Illinois delegation over soggy scrambled eggs. "I am genuinely thrilled by your expertise and concern," said Thompson - then asked their help in passing the energy bill and urging that some of the well-head tax money get back to the states.After his breakfast rhetoric. Thompson said, "I'm going to work out a three part slogan for myself and any other candidates - don't raise taxes, cut welfare fraud and keep your mouth shut."

Thompson then rushed to make a one-hour appearance at a full meeting of the governors on urban crisis before his run to the airport. He had a press waiting in Illinois to brief on his budget (balancedagain) to be submitted today.

At the final D.C. meeting Thompson, did not talk with Gov. George Wallace, who sat next to him and blew smoke from a ciger in his direction. Thompson talked instead to the aides who knelt by his side and his 31-year old pregnant wife, who sat behind.

A former student of his at North-western University Law School, she became Thompson's assistant when he was attonrey general. She is already a correct political wife - "I don't comment on political issues. I didn't trun. My views are irrelevant."

"There goes Gov. Thompson," says a reporter, but does not chase him. Nor does Thompson stop.

All the while Jerry Brown is at the old stand - talking into a TV camera then whipping around to the press room to cut a tape. Six reporters stand in line with tape recorders in hand.

Meanwhile, Thompson was out the door.