The prime minister said on Saturday he expected there to be some "bumpy" months ahead and claimed to be “working flat-out” to make Christmas as normal as possible.
Johnson, who has previously accused members of the public of being "complacent" over the virus, said people needed to act responsibly in order to contain the virus and keep the economy going.
Johnson said: "If you ask me 'do I think things can be significantly different by Christmas?' Yes I do, and we're working flat-out to achieve that.
"But be in no doubt that it is still very possible that there are bumpy, bumpy months ahead. This could be a very tough winter for all of us - we've got to face that fact."
Johnson suggested the picture could be "radically different" by spring 2021.
The prime minister acknowledged that people were "furious" with him and his government over the handling of the pandemic.
He said: "I appreciate the fatigue that people are experiencing... but we have to work together, follow the guidance and get the virus down whilst keeping the economy moving."
Johnson defended the 10pm curfew, which has seen crowded scenes as drinkers and diners leave bars and restaurants at the same time.
"Obviously it makes no sense if, having followed the guidance for all the time in the pub they then pour out into the street and hobnob in such a way as to spread the virus."
Measures such as the curfew have fuelled Tory resentment from influential MPs including Steve Baker and 1922 Committee chairman Sir Graham Brady about restrictions which have caused widespread economic damage.
Johnson said: "I'm a freedom-loving Tory. I don't want to have to impose measures like this, are you crazy?
"This is the last thing we want to do. But I also have to save life. And that's our priority."
Coronavirus: what happened today