According to White House officials yesterday, the short list for what will be the first Court appointment by a Democratic president in a quarter of a century has been narrowed to three: Mr Babbitt, a former governor of Arizona and briefly a Democratic presidential contender in 1988, and two widely esteemed and moderate Appeals Court judges, Stephen Breyer of Boston and Gilbert Merritt, chief judge of the US 6th Circuit Court of Appeals in Cincinnati.
In an ideal world, the much admired Mr Babbitt would be a supremely logical choice. His background, admittedly, is far more that of politician than jurist. But he is a pragmatist from the centre of his party, whose pro-abortion, pro-civil rights views would produce exactly the liberal shift in the Court's centre of gravity Mr Clinton is seeking. But times for this beleaguered President are anything but ideal.
As he struggles to regain his footing after a string of blunders culminating in last week's debacle over Lani Guinier, and searches for a compromise to save his all-important deficit-cutting plan in the Senate this month, the last thing Mr Clinton needs is a fight over a Supreme Court nomination. But clouds were gathering yesterday.
Among them was resurrection by the right-wing press of allegations over Las Vegas gambling debts and mob payoffs by Mr Babbitt, which he describes as 'nonsense'. Another was mutterings from Republicans on the Senate Judiciary Committee, which has to approve the nomination, that Mr Babbitt might try to impose his political views rather than the law. The confirmation of either Mr Breyer or Mr Merritt, by contrast, is held to be virtually automatic.
Most serious is the price Mr Clinton would pay in the electorally vital West and in the environmental community, both of which see Mr Babbitt as their champion in the cabinet. As one leading wildlife activist put it: 'He's basically irreplaceable at Interior.' If he does move, moreover, Mr Clinton would have the time-consuming task of finding another Interior Secretary. By some accounts, the process has already started.
In the meantime, the President's scramble back to the political centre continues. Yesterday, at a 'cordial' meeting with Republican and Democrat congressional leaders, he again signalled his willingness to amend the budget package by scaling down his energy tax and making deeper spending cuts.
Conciliation is also the order of the hour in the White House press room, among Mr Clinton's prime tormentors in his four troubled months in office. The affable Mark Gearan has replaced the heartily disliked George Stephanopoulos as communications director, and in a first symbolic move ordered reporters once more be allowed free access to the press office.
But nomination difficulties continue to dog the President. It now emerges that the Mayor of Boston, Ray Flynn, may turn down the job of US envoy to the Vatican he was offered three months ago. Mr Flynn is reportedly furious that orginal promises he would be a roving human rights ambassador have been withdrawn, and that the State Department vetoed a dollars 500,000 (pounds 330,000) fundraising event by his supporters.
Mr Flynn, who has six children and earns dollars 115,000 as mayor, says he does not have the means to pay for the entertaining that goes with the Vatican post out of his own pocket.