Prominent legal and police figures have derided the proposal as ineffective and political demagoguery.
The Attorney-General, Janet Reno, has voiced fears about such a blanket response to frequent offenders, and in Congress, some black Democrats have tentatively raised civil rights concerns.
Several versions of the 'three strikes' provision are under consideration but, in essence, anyone found guilty of a committing a violent, federal offence, who has been convicted of two previous crimes, not necessarily violent in nature, would be incarcerated for good.
By embracing such a proposal, Mr Clinton deliberately identified himself with the hard-line conservative school on combating crime.
He is not only following the popular trend - crime is overtaking the economy as the main object of anxiety among Americans - but is also stealing some thunder from the Republicans.
That the response from liberals within the President's own party has been so muted is testament to the strength of public support. Momentum behind the 'three strikes' provision seems unstoppable, and no fewer than 30 states are considering introducing such legislation.
It did not go unnoticed, however, that while both sides of the chamber gave a standing ovation to the proposal, members of the congressional black caucus remained seated. Before his speech, caucus members wrote to the President asking him to 'blend the need for certain and severe punishment for today's most serious offenders with the need for compassion and community-building'.
The black New York Democrat Charles Rangel fears that 'small-time punks, mixed-up kids' could be ensnared. And similar worries have been raised by the American Civil Liberties Union, which is leading opposition to the provision.
Eric Sterling of the Criminal Justice Policy Foundation dismisses the measures as 'a vote-getting, headline-getting policy'. 'This provision, instead of targeting rapists, armed robbers or serial killers, will send to prison for life the punk who has a fight outside a bar after his team loses the Super Bowl, the drug-addict burglar and a host of penny-ante offenders.'