The first hint that Mrs Clinton's four months of cogitation were at an end came early yesterday afternoon when Nita Lowey, the New York Congresswoman who had planned to run for the Senate, announced that she would run for re-election to the House instead. Mrs Clinton had promised that she would talk to Ms Lowey before making her intentions known. In the event, Ms Lowey called her to clear her way. A spokesman for Ms Lowey said she had told Mrs Clinton that she had decided to seek re-election to the House of Representatives in 2000 because "it was clear to her that the First Lady was running". The statement said that "she wished the First Lady well and would support her candidacy and do everything she could to help elect her to the Senate".
Mrs Clinton had "thanked Nita for her friendship, said she had been wonderful during these last several months and said she looked forward to working with her".
Mrs Clinton has travelled to New York twice in the past week, the first time for a fund-raising dinner for Ms Lowey.
The Senate seat is to be vacated by the veteran Democrat, Daniel Pat Moynihan. Last November, Charles Schumer, a Democrat, wrested the other New York Senate seat from Alfonse D'Amato, who had held it for 18 years.
Mrs Clinton would be the first President's wife to opt for political office in her own right. A similar proposition was made to Eleanor Roosevelt, but she declined, reportedly without giving it a second thought.
Democrats are hopeful that Mr Schumer's unexpectedly clear victory over Mr D'Amato represents a turn of the Republican tide in New York and that Mrs Clinton - a celebrity candidate if ever there was one - will appeal to New Yorker voters. A highly effective campaigner for whom public sympathy soared over her handling of the Lewinsky affair, Mrs Clinton is credited with having helped several Democratic candidates, including Mr Schumer, to victory in last year's Congressional elections.
Mr Giuliani, in contrast, has recently experienced a reversal in his popularity. Two cases of police brutality caused an outcry and suggested that his stringent law and order policy had gone further than New Yorkers would tolerate.
Recent opinion polls have varied wildly as to who would emerge the victor, but the consensus is that Mrs Clinton has more than a sporting chance. Those expressing misgivings question above all the propriety of a First Lady running for office while still at the White House.
President Clinton, however, appears to have no qualms.