Frank Dobson, the former health secretary, has described it as "one of the growing products of the fact the Prime Minister is going, and his authority isn't as strong as it used to be".
That a relatively small issue such as smoking could bring government business to a shuddering halt is a sign that ministers are breaking out of collective discipline to mark out their territories. The biggest fault line in the Cabinet is over Mr Blair's determination to reform public services, introducing the private sector to schools and family doctor services, before he leaves, to secure his legacy and prevent his successor, Gordon Brown, from abandoning the political ground he has captured.
The tension has been exacerbated by the rise of David Cameron in the Tory party, who walks and talks like Mr Blair, and promises to side with the Prime Minister whenever he is in conflict with the Chancellor, the trade unions, or the Labour Party. "We are looking at a grand coalition of Blair and Cameron against the Labour Party," said a minister.
Ironically, the main antagonists in the smoking dispute - the Defence Secretary John Reid, and the Culture Secretary, Tessa Jowell, are part of Mr Blair's praetorian guard who helped to persuade him to stay on in 2004, when he contemplated resignation. Both agree with the Blairite maxim that Labour is "at its best when it's at its boldest".
For Ms Jowell "boldness" means radical action to protect public health, while for Mr Reid it means being prepared to face down the "learned middle class" and think of "the '21-year-old single mother-of-three living in a council sink estate".
Yesterday, some of Mr Brown's allies scarcely troubled to conceal how much they were enjoying this spat between Blairites, especially since it has been left to the Foreign Secretary, Jack Straw - a Brown ally - to "broker a deal between the warring factions", as one of his aides put it.
Ms Hewitt, the Health Secretary, who is caught in the middle of the smoking row, is another ultra-Blairite, who is driving forward with health reforms that threaten to expose another fault line in the Cabinet. Earlier this month, she was given one of the worst receptions ever suffered by any cabinet ministers at the regular private weekly meetings of Labour MPs. According to witnesses, 19 MPs attacked her proposed reforms of the NHS, and not one spoke in her defence.
"That's never happened before in my time in Parliament," a whip said later. More dangerously for Mr Blair, his loyal deputy John Prescott stood up to him over the education White Paper published this week by Ruth Kelly. Some of Mr Brown's allies grumble that Mr Prescott accepted a compromise. They want him to use his muscle to punch holes in the health White Paper in December.
In both cases, Labour MPs complain Blair's sole concern is to hold on to middle-class votes that might go to the Tories.
One leading backbench MP said: "The great thing about New Labour was that it appealed to the middle classes and looked after people like my constituents. Now we're abandoning half of that settlement.
"And if a New Labour MP like me is saying that, you know that there's trouble coming."
Where the fault lines fall
Anxieties: John Prescott, Deputy Prime Minister; Gordon Brown, Chancellor; Patricia Hewitt, Health Secretary; Geoff Hoon, Leader of the House.
For tougher ban: Culture Secretary Tessa Jowell; Patricia Hewitt (non-smokers)
For more exemptions: John Reid, Defence Secretary (reformed smoker); Tony Blair.
HEALTH SERVICES OUTSIDE HOSPITALS
Expected to oppose wider use of private sector: John Prescott, Gordon Brown.
For radical reform: Patricia Hewitt; John Reid; Charles Clarke; Home Secretary.