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As Carol Moseley Braun was beginning her bid for the Democratic Senate nomination in December, it was widely viewed as an impossible dream.

Braun, after all, was merely a glorified clerk, the head of a Cook County office responsible for recording real estate transactions. Furthermore, she is an African-American woman, a combination that had never before been nominated for a Senate seat by a major party, much less sent to Washington by voters.

Her opponents were not exactly pushovers, either. The incumbent, Sen. Alan Dixon, had won every election in 42 years in politics and was seen as so formidable that none of the most prominent Republicans in the state wanted to take him on in the general election.

And although largely unknown outside of legal circles, the third person in the race, Chicago lawyer Albert Hofeld, was prepared to spend millions of his own dollars to get his message across, which, in the age of big-bucks television advertising, scared even a battle-scarred veteran like Dixon.

Yet three months later, it is Braun, not Dixon or Hofeld, who has won the political battle of her career and is preparing to try to do it again.

Her upset in Tuesday`s primary befuddled the Illinois political brain trust and invigorated the true believers. Women from all walks of life reported crying tears of joy as they watched Braun give her victory speech that night.

Braun`s triumph also means that the state`s Senate race will become one of the most intensely fought in the nation.

Republicans suddenly believe they can win a seat they had written off, and Democrats-especially women and black Democrats-see the best chance in history to alter the makeup of a body nearly as exclusive as the most racist, sexist country clubs.

But for all the sense of history now attached to her, the political campaign that catapulted Braun into a national celebrity was hardly a thing of beauty. It lurched along, shedding key advisers along the way, and was held together primarily by Braun`s belief in herself and by her unwillingness to pander to blacks, women or people upset at the confirmation hearings for Clarence Thomas to be a justice on the U.S. Supreme Court.

A narrow-eyed analysis of how she won reveals a series of happy coincidences that played as large a role as anything the campaign planned on. Everything, from anti-incumbency fervor to the Thomas hearings to a series of key Senate votes that kept Dixon in Washington for six of the campaign`s last 14 days, contributed.

And probably the biggest factor was the good luck Braun had in having a rich man in the race who had to be on TV all the time, both to make himself known and to sully the incumbent.

The Hofeld campaign`s bashing of Dixon for three months reminded Democratic voters, over and over again, of the incumbent`s ties to the system and his conservative voting record.

It sent Dixon into a tailspin in the final weeks of the campaign that no amount of campaigning or response ads could overcome.

”Three things happened late in the game,” said Don Rose, a veteran Chicago political consultant. ”The black vote consolidated and the women`s vote developed, which has been one of those things that have been threatened for 10 years, and it finally really happened, including crossovers.”

Crossovers are Republican women who took Democratic ballots to vote for Braun. ”More importantly, the beating that Dixon was taking finally put him into a free fall,” Rose said.

A graduate of the University of Chicago Law School and a former federal prosecutor who got into politics almost by accident, Braun for years had considered running for the U.S. House of Representatives.

But it was the spectacle of the Thomas hearings, with the sexual-harassment allegations by Anita Hill, that pushed her into the Senate race, Braun said.

It wasn`t so much the vote of Dixon to confirm Thomas, although that contributed, but the sight of an all-white, virtually all-male Senate, Braun has said. Not only did that dramatize questions already in her mind about how representative such a body could be, but it caused many female activists and a fair number of men to urge her into the race.

By November, she had made up her mind to heed them. It was a move that surprised many who had followed Braun`s career. From the start, she had adhered to most Democratic Party rules, eventually rising in the Illinois House, where she served 10 years, to be assistant majority leader under Speaker Michael Madigan.

Challenging a two-term incumbent senator, the third-ranking Democrat in the Senate, broke those rules, although there is a clear parallel between it and her decision to be an early supporter of Harold Washington`s outsider bid for mayor in 1983.

Dixon, she said, was not a true Democrat. Indeed, in 1991 he had voted with the Bush administration more than any other Northern Democrat.

Meanwhile, Braun, 44, had long worn the tag of overwhelming political promise on her lapel, but she had passed on two opportunities to run for lieutenant governor and her current job had hardly positioned her for anything significant in the future.

Indeed, speculation outside the Braun campaign centered on which political office she wanted her quixotic bid for Senate to set her up for:

Chicago mayor? Illinois attorney general? The 1st Congressional District seat when Rep. Charles Hayes decided to retire?

Inside the campaign, though, there was no such talk, said Alton Miller, Braun`s communications director for much of the campaign. ”She denied it candidly, convincingly, in private as well as in public,” he said. ”She really wanted to run for the Senate.”

The campaign deep thinkers, Miller said, theorized back in December that it was important for Hofeld to earn around 28 percent of the vote, which he did. They figured this would bring Dixon`s numbers down to somewhere in that ballpark, which it did. And they thought Braun might squeak by with about 34 percent of the vote. She finished with 38 percent to Dixon`s 35 percent.

”In the meantime, we knew she could walk into a living room or a shopping mall and there was this movement just ready for the touch,” Miller said. ”The people who analyzed the polls for us said, `This election is going to be won with white women, period.`

”That is a deprecatingly simplistic analysis of the fact, but it is a mistake to look at her and say her base is the South Side of Chicago. We started saying white women and what I call the Alan Alda factor . . . people who respond to the idea that a senator doesn`t have to be 6 feet 2 and graying at the temples and, by the way, white and male.”

There were internal discussions among Braun`s staff about whether she should tailor the speeches she delivered to black voters.

Kgosie Matthews, her campaign manager, disagreed with that position, said Timuel Black, a South Side organizer and the campaign`s co-chairperson.

”Finally there was agreement that she should stay general and be consistent as her message related to unemployment, education and other issues that affect everyone, including the black community,” Black said.

By keeping her message as wide as possible and not varying it, Braun kept from alienating white voters while holding on to her black support.

And while there were some supporters who suggested that Braun bring in Jesse Jackson or Hill to campaign for her, her campaign staff decided it was best to keep such controversial celebrities out in order not to give people any reasons not to vote for her.

Braun also helped herself by failing to emphasize the Thomas vote in her campaigning, said Rose.

Harping on that, he said, could only make her campaign seem less senatorial, more single-minded. ”I`ve seen time and again candidates who will take a reason for their base and just dig a trench for themselves,” Rose said.

Braun insisted on campaigning Downstate, Miller said, when her pollsters were advising her to focus on Cook County and the Chicago suburbs. And she did surprisingly well there, especially in university counties. In Champaign County, home of the University of Illinois, she earned almost as many votes as her two opponents combined.

Although Dixon`s tracking polls showed Braun surging in the final full week of the campaign, his advisers believed her support had peaked by midweek. The campaign stopped polling the night of March 12 because there was no money left, said Steve Rabinowitz, a Dixon consultant.

And although Hofeld, 55, did attack her toward the end, Dixon, 64, resisted suggestions by some aides that he do the same.

Much has been written about Braun staying above the fray, and the perception that she did so helped her. But in appearances, she would repeatedly charge that Dixon was ”voting the weather map” rather than his conscience and that Hofeld was a millionaire trying to buy the election.

Yet her campaign often appeared to be running on three wheels.

Of six top advisers who were in on the early strategy sessions, Miller said, just two were there at the end. Miller was not among them.

Most were reportedly put off by the autocratic style of Matthews, who had never run a major campaign.

But while political observers note that it was not a well-executed campaign, Braun`s natural constituencies and her warmth generated the kind of excitement that other campaigns create via events and revelations about opponents.

An ingredient in Braun`s success that can`t be understated is Braun herself. On the stump and in the campaign`s only debate, she came across as bright, friendly, well-spoken, humorous and down to earth.

And though she has been in public life for almost 15 years, she was a relatively fresh face.

”What she did right is to not be strident and to be the warm, infectiously gracious person she is, which is the best asset she`s had,” said Tom Roeser, a conservative political commentator and a supporter of Braun`s November opponent, Kenilworth lawyer Richard Williamson.

”With two white guys beating themselves over the head and the women out there wanting to turn this away from a male club, she benefited very well.”

Janice Schakowsky, a North Shore state representative and Braun organizer, was more succinct: ”When people see her, they love her,” she said.

The problem was seeing her.

Perhaps the greatest irony of the underfunded Braun campaign-it spent $440,000 compared with Dixon`s $2.1 million and Hofeld`s $4.7 million-was that it had a telegenic candidate who couldn`t get on TV. Only in the last days of the campaign did it air a pair of low-budget ads in low-budget time slots.

So the campaign resorted to a pre-television style campaign. Running on a manic schedule, especially in the last two weeks, she tried to outhustle her opponents, speaking to more groups and shaking more hands.

”She basically was forced into using old techniques: going out into the street, meeting people, traveling all over and not doing 30-second sound bites,” said Twiley Barker, a professor of political science at the University of Illinois at Chicago who taught Braun when she was a student.

Barker said he believes Braun`s throwback campaign came along when voters were tiring of slickly packaged TV campaigns.

Because of Braun`s surprising success, ”we may begin to see a new kind of campaign style that emphasizes more direct contact with voters instead of all the spending on electronic media,” said Barker.

Going door-to-door for votes meant Braun was constantly in motion as she tried to cover as much ground as possible to get out her message that it was time to make history.

”We knew we had a star,” said Larry Shapiro, a Braun campaign adviser.

”We just had to put her up on stage and keep moving the stage.”