In a dramatic about turn, Mr Johnson told MPs the new system could last just nine weeks and offered them another vote on the restrictions at the start of February.
But Tory MPs warned the shift has yet to quell the rebellion.
Pauline Latham, the Conservative MP for Mid-Derbyshire, said she "might" support the government in this week’s vote on the tiered measures if "more evidence" was laid out.
She told Sky's Sophy Ridge On Sunday: "I think it will depend very much on what Boris does between now and Tuesday.
"If he produces that evidence and he can prove to us that he's got good evidence to go on then I think he won't have a rebellion."
She said people were “not happy" and that MPs were "reflecting what their constituents are saying to them".
Earlier Foreign secretary Dominic Raab raised the spectre of a return to national lockdown as he defended the new tiers.
The rules were necessary to "bear down" on the pandemic, he told the BBC’s Andrew Marr programme.
He said the government was trying to come out of a national lockdown “and stay out” and warned of the “risk” of a third wave of Covid-19 if ministers did not get the virus under control.
Later when asked on Times Radio if the government intended to stick to the county by county system of Covid tiers, he said "That's the approach we're taking. Yes."
Tory MP and former children’s minister Tim Loughton said that unless MPs received the cost-benefit analysis they have asked for between now and Tuesday the prime minister’s letter offering a new sunset clause “does not change anything, I’m afraid.”
Mark Harper, the chair of the Covid Recovery Group of Tory MPs, said: “We need hard evidence not hyperbole”.
“Show us that the measures that are being proposed are going to be effective and show us the cost of those measures”.
Last week 70 members of the group wrote to the prime minister asking him to set out the cost-benefit analysis of the tiers.
Downing Street has said the information will be made available before Tuesday’s vote.
Mr Harper also said that in some parts of England a county-by-county approach was “sensible, but I can see in some parts of the country where you have much bigger variance… that might not actually be sensible”.
Steve Baker, another member of the CRG, told the Mail on Sunday that he and others would “digest” the climdown over the weekend, but called on No10 to publish a full analysis of the “health, economic and social impacts of Covid and the measures taken to suppress them”.
In the same newspaper Mr Johnson urged his MPs to back the measures.
He wrote: “It is crucial to understand that with the help of these scientific advances we hope to make progress - and to de-escalate - BEFORE Easter.”
He added that the new restrictions in place from Wednesday would not be a lockdown.
“You will be able to leave your home for any reason. You can do your Christmas shopping, indeed any type of shopping; visit the gym; have a haircut; play organised sports; take part in communal worship; and meet friends in outside public places subject to the rule of six.
“We are so nearly out of our captivity. We can see the sunlit upland pastures ahead. But if we try to jump the fence now, we will simply tangle ourselves in the last barbed wire, with disastrous consequences for the NHS.”
There was also anger at reports the health minister Nadine Dorries told a group of Tory MPs the much-heralded Nightingale hospitals, built to help the NHS deal with extra Covid cases, were largely empty because people regarded them as "dark and dingy".