The first, emotional, response from Americans seemed to be that he could. But even after his admission of an "inappropriate relationship" with Monica Lewinsky, Mr Clinton faces the very same two problems as existed back in January when the allegations about his relationship first surfaced. The first is the legal question of whether he committed perjury or not when he denied an affair. The second is the political question of his credibility with the voters after so sharp a reversal of his position.
Mr Clinton had hoped to quash the perjury accusations once and for all by insisting that what he told the Paula Jones sexual harassment lawyers under oath was "technically correct". But he did admit that he did "not volunteer" information. This may not amount to perjury, but questions were asked yesterday about the indefiniteness of other responses in that investigation.
When he repeatedly said that he did not "recall" or "recollect" specific incidents or occasions - like being alone with Ms Lewinsky, like giving her gifts - could this amount to perjury? This is a question for the independent prosecutor, Kenneth Starr, and for Congress, but he may not be off the perjury hook yet.
Of the other accusations being investigated by Mr Starr, one - that Mr Clinton may have obstructed the course of justice or suborned perjury by instructing Ms Lewinsky to lie about the relationship under oath - seems to have been quashed by Ms Lewinsky's testimony.
Allegations of "witness-tampering", however, which include settling Ms Lewinsky and others of his accusers in plum jobs or threatening less co-operative individuals with "being destroyed" if they told the truth, could be less easy to deflect. These accusations were not addressed in the statements of either Mr Clinton or his lawyer.
If anything finishes off Bill Clinton's presidency before time, however, it will probably be the political liability of his starkly conflicting television statements. On 26 January, Mr Clinton jabbed his finger at the camera and - as one commentator said - "lied to us". "I want you to listen to me," he said. "I'm going to say this again: I did not have sexual relations with that woman, Ms Lewinsky." On 17 August, he admitted: "I did have a relationship with Miss Lewinsky that was not appropriate. In fact, it was wrong."
In Britain, no politician, let along the national leader, would survive an admission like that, penitent or not, whether the accusation related to his private life or not. It would be the lie, not the relationship, that damned him, and no squealing about private life being private would save him.