A White House spokeswoman said the President would designate a new head of the Justice Department 'soon'. But, despite predictable fresh pressure from women's lobbies, it was unclear whether he would stick to his proclaimed goal of choosing a first-ever female to head what is traditionally viewed as one of the four most important cabinet posts.
Mr Clinton's weary, pouchy face at yesterday's swearing-in for all but two of the 18-strong cabinet - a ceremony signifying that the great pageant of the inauguration is finally over, and that the mundane, day-to-day process of governing has begun - was testament to the unwanted mini-crisis of the previous night.
The clouds had steadily darkened throughout Thursday, as outrage grew over Mrs Baird's admission she had employed a Peruvian couple of illegal aliens as live-in domestic servants for the best part of two years, and then compounded the misdeed by failing to pay required Social Security contributions. Poll after poll showed public opinion overwhelmingly against her.
Chastened by the 1991 uproar over its insensitive handling of the Clarence Thomas/Anita Hill affair, the Senate Judiciary Committee was in no mood to disagree. In increasing numbers, key senators, Republicans and Democrats alike, withdrew their previous backing. By 9.30pm, when the confirmation hearing ended, it was obvious she was doomed. A midnight exchange of letters between Mr Clinton and his nominee merely sealed the inevitable.
Professing 'surprise at the extent of public reaction', Mrs Baird acknowledged that the controversy 'seriously impeded' her chances of revitalising the Justice Department. The President expressed sadness at the move, describing Mrs Baird as a woman of 'decency and integrity'. But he admitted that mistakes had been made by his transition staff, who were aware of the problem. 'For that I take full responsibility,' he said.
And that indeed is the main question raised by the affair: did Mr Clinton himself know of Mrs Baird's offence before announcing her nomination on 24 December? And, if so, how did he so badly misread public opinion as to assume it would be forgiven and forgotten? The answers provided by his novice team of spokesmen have been, to put it mildly, conflicting.
But the embarrassment should not cause lasting damage. Mr Clinton has moved quickly to regain momentum with executive orders lifting various abortion curbs imposed by George Bush, notably the 'gag rule' banning abortion counselling at federal clinics. 'This fuss wasn't a political struggle,' said Thomas Mann, head of the Government studies department at the Brookings Institution. 'Clinton expended very little political capital.'
And, indeed, the White House gave only lukewarm support to Mrs Baird as her troubles mounted, and made no attempt to lobby senators in the style of Mr Bush four years ago, before the infinitely more serious defeat he suffered when the Senate voted down John Tower, his first nominee for defence secretary.
The outcome of that affair, moreover, might encourage Mr Clinton in his search for a new broom to sweep away the reputation for incompetence, infighting and right-wing ideological crusading which the Justice Department gained during the 12-year Reagan/Bush era. Mr Tower's replacement, Dick Cheney, turned out to be one of the most effective defence secretaries in decades, and is considered a front runner for the Republican presidential nomination in 1996.
On Capitol Hill, the feeling was of relief. 'They made the right decision,' said Tom Foley, the Democratic Speaker of the House, while the Republican senator Alan Simpson of Wyoming - who wrote the immigration law Mrs Baird broke - agreed: 'This a good message to send to the country.'
Confirmation of Mrs Baird as the chief law enforcement officer in the US would have been in flagrant violation of the spirit of the strict new ethics code Mr Clinton has imposed on his cabinet and left the impression that, for all the dissatisfaction with Washington so evident in the election campaign, in the corridors of power it was still 'business as usual'. There was no immediate clue to Mrs Baird's successor. Mr Clinton could make another effort to persuade the US District Judge, Patricia Wald, his first choice for the post, to reconsider her earlier refusal. Peter Edelman, who ran his Justice Department transition team, is another name being mentioned.