It was apparently late Wednesday night, unseasonably chilly even for November, when Prime Minister Margaret Thatcher faced the cold reality that most of her party wanted her to quit. Only hours before, she had strode confidently from 10 Downing Street, the official residence, to say she was intent on beating Michael Heseltine, the former defense secretary who had challenged her for leadership of the governing Conservative Party. ``I fight on, I fight to win!'' she had declared. According to statements by aides and allies, as well as accounts in Friday's newspapers, it was all downhill from there. The prime minister seemed in good form earlier Wednesday in the House of Commons, delivering a report on the European security summit in Paris. Then she surprised lawmakers with a rare appearance in the Commons' tearoom to solicit support. Later, in her office at the House of Commons, she met one by one with a succession of Cabinet ministers and old allies. Most delivered the same brutal message: the rank-and-file were defecting after Mrs. Thatcher's failure to dispatch Heseltine cleanly in the first round of a party leadership vote. ``It's a funny old world,'' she told some of her messengers, according to The Times and The Daily Telegraph. Only a few of her staunchest allies encouraged the prime minister to push on. ``It took just a few hours for Mrs. Thatcher to realize she had lost touch with reality, that her supporters on the right of the party were seeing the world through eyes focused on her earlier triumphs,'' wrote Philip Stephens, the respected political writer of The Financial Times. To Thatcher loyalists, it looked like a palace coup. ``It's rank treachery. Our own people have done it,'' complained Tory lawmaker Edward Leigh. The agony began Tuesday evening when Mrs. Thatcher, in Paris for the 34-nation security summit, learned that she had narrowly failed to gain the margin of 56 votes needed to beat Heseltine in round one that day. Of the 372 Tory lawmakers, 204 voted for the prime minister, 152 for Heseltine and 16 abstained. She responded within minutes. ``Look, I have more than half the votes of the parliamentary party. It was not quite 15 percent above those of Mr. Heseltine. ... so it means we have to go forward for a second ballot,'' she told reporters. She then changed into a formal gown to join other government leaders for ballet and dinner at Versailles. She arrived a few minutes late, smiling radiantly. But she was sufficiently rattled to leave the summit early. Returning to London at midday Wednesday, she sacked her campaign manager and began drawing up new battle plans. She received some welcome advice from staunch allies Norman Tebbit and party chairman Kenneth Baker. According to Stephens, they convinced her that her first-round failure was simply ``due to a lack of lack of organization and commitment,'' and predicted she would win on the second ballot, when all she needed was an outright majority. But the Cabinet reportedly was becoming increasingly mutinous. John MacGregor, the leader of the House of Commons, ascertained that 12 of 21 Cabinet ministers thought Mrs. Thatcher should resign, Stephens said. Mrs. Thatcher, however, reportedly seized on the upbeat report from Tebbit and Baker. When Tim Renton, the government's chief vote-counter in the House of Commons, told her the rank-and-file support was collapsing, Stephens said that she snapped: ``Who else can beat Heseltine?'' That evening, in those one-on-one meetings, The Times said she old one visitor: ``I am coming under an awful lot of pressure.'' The final blow, according to Stephens, was delivered by John Wakeham, whom Mrs. Thatcher had installed earlier in the day to direct her campaign. Wakeham is an old and trusted friend. His first wife was one of five people killed in 1984 by an Irish Republican Army bomb that ripped through a hotel where Mrs. Thatcher was attending a party conference. ``Wakeham ... came back to report his soundings among members of parliament. Yes, the Cabinet was right. She had to withdraw,'' Stephens said. The next morning, she made the announcement to her Cabinet.