Furious Tory MPs had lined up to say they would vote against plans to put 99 per cent of the country in the two tiers with the most severe restrictions.
The system had been expected to last until the end of March.
However, in a significant climbdown the prime minister has now written to all MPs telling them that if they back the measure this week a new sunset clause will mean the restrictions last only until the start of February.
At that stage MPs would have another vote on the tiers, which would determine whether or not they stay in place until the end of March.
The prime minister also pledged to publish advice on what would need to change in every local area to allow it to move down a tier.
A bleak warning that every hospital in England risks being overwhelmed by Covid-19 cases had earlier failed to quell the rebellion.
Cabinet Office minister Michael Gove had urged Tory MPs to "take responsibility for difficult decisions" to curb the spread of the virus.
He warned it was “no respecter of constituency boundaries” and hardships were “unfortunately necessary to protect every single one of us, no matter where we live” in an article for The Times.
But dozens of Tory MPs were still expected to refuse to back the new system, in a major challenge to Mr Johnson’s authority.
Many are angry that much of England will be placed in the top two tiers which face the toughest coronavirus restrictions, including on households mixing indoors.
The chairman of the powerful backbench 1922 Committee of Tory MPs, Sir Graham Brady, was among those who expressed his opposition to the new tiers, calling for the public to be "treated as adults" and trusted with their own health decisions.
Other Tory MPs had indicated that they would rebel if an assessment due to be published next week was not convincing.
Some have called for the system to be more targeted. They complain that areas with tiny infection rates have been unfairly lumped in with others where cases are sky high.
But ministers warn cases can quickly shoot up in areas which attract large numbers of visitors.
As the government’s woes grew Labour remained tightlipped on how it might vote on the measures on Tuesday.
Meanwhile, Conservative former health secretary Lord Lansley said Mr Johnson was "wrong" to relax coronavirus restrictions over Christmas.
He admitted that saying so made him "feel like the grinch", but in an interview with Times Radio he said: "We've got to protect old people. And it really is difficult, I think, to suddenly say Christmas, well, let's not do that. Let's allow people to mix. Why would we do that?
"We are potentially only maybe weeks, well, perhaps months, but not many months away from the point at which we may be able to vaccinate the most vulnerable and our oldest population?
"Why expose them to any risk in that period? Why allow transmission potentially to accelerate even for a short period?"