The hosts once again need to produce something special to keep the series alive as they head into the final day of the fourth Test against Australia.
England reached the close on Saturday on 18 for two, chasing a distant 383 to win or, more realistically, needing to bat three sessions to escape with a draw.
It is a tall order, but with memories of Ben Stokes’ stunning match-winning hundred in Leeds a fortnight ago still fresh, England will not throw the towel in.
Bayliss said: “It’s a big challenge but we’ve got two guys out there who are very good players and we’ve certainly got some players in the sheds who can make hundreds.
“It’ll take a couple of our guys to make good hundreds but, as we saw in the last Test, anything is possible.
“I’m always positive, I think we can do it. We’ve had a chat in the changing room, we’re certainly not going out thinking it’s all over. They believe they are good enough to bat for 98 overs and save the game.”
England made a dreadful start in their rearguard action as they lost opener Rory Burns and captain Joe Root without a run on the board. Joe Denly and Jason Roy will be the men to resume on Sunday morning.
Bayliss is confident in the batsmen remaining and points to Stokes’ heroic efforts as proof of what can be achieved.
He said: “It probably gives the rest of the guys belief, that if one guy can do it someone else can do it as well.
“We’ve already spoken about who is going to put their hand up and be the hero tomorrow. We know it is going to be hard work, but we’re going out there with the aim to do that.”
Australia have got themselves into such a strong position largely due to the performance of Steve Smith.
Smith hit a double century in the first innings and then followed up with 82 in the second - remarkably his lowest score of the series in five innings - as Australia set their target by posting 186 for six declared.
Smith said: “When it is tough you want your experienced players to step up. I have played quite a lot of cricket now. I like to get in those situations and try to be the one to take the team through.
“I was able to form a really good partnership with Matty Wade, hopefully one that sets us up for this game.”
Australia need to take eight wickets on Sunday to win the match and claim the Ashes. As the holders, a 2-1 series lead would secure the urn regardless of the result in the final Test at the Oval next week.
Smith said: “For us it is pretty clear what we need to do - quicks hit a good length, Gazza (Nathan Lyon) hit the rough as much as possible.
“It is just about relaxing and going out and enjoying it and hopefully executing our skills well enough to bowl England out tomorrow.”