The back-to-back champions have lost two successive games in their qualifying pool, but know that two bonus-point wins from their final two games against Scarlets and Exeter, and favourable results elsewhere, could seal an improbable quarter-final berth.
"I might be naive, but I do believe in miracles," declared the bullish Kiwi as he prepares for the first time this season to lead a full-strength Leinster side into Europe at the RDS tomorrow.
"That's one of the reasons people love sport. They love it because they want to see the miracle. And they don't come up too often, so you treasure them when they happen.
"We've had a couple of them in the last couple of years that will certainly be indelibly etched in my memory and I'd love to get another very good memory in the next two weeks. But at the moment it's all in front of us, so we're not really chasing miracles, we're just chasing an accurate line-out and we'll play off that, and try to build the process if trying to get to the end result."
Leinster may need successive four-try bonus point wins to qualify but, although they have only scored three tries in their opening four matches so far, Schmidt points to the last two final successes, against Northampton and Ulster, to justify his optimism.
"It might not come in the first 40 minutes, but that doesn't mean it's not going to come," he says.
"It's about trying to keep the confidence up when we might not even be in front at half-time. We might not even have a try on the board. We'd certainly like to.
"But we have that confidence that we can get tries in the second-half. We got three tries in the second-halves of the last two Heineken Cup finals. It's something that we feel is not beyond us."
O'Callaghan has instead challenged the players to repay the faith shown in them by Rob Penney and his coaches as Munster prepare for what is a season-defining game against Edinburgh on Sunday afternoon.
"I'll be honest, from a player's point of view, you almost feel like you owe the coaches one," said O'Callaghan. "There's a lot of talk about how we're playing the game and the different shape but we know when you play any game plan poorly it looks poor.
"Rob is good for standing up for us, but Sunday, at quarter to one, we have to stand up for him," added O'Callaghan.
That Munster made a massive 29 errors in the Pro12 game against Cardiff Blues has been a cause of some concern in the camp this week and O'Callaghan has urged the players to take ownership of their own failings.
"Dropped balls, what do you put them down to? Fellas running into touch? It's just soft. Anthony Foley goes on about the touchline being the best defender on the pitch and we know better than anyone that when you're on the attack, you stay away from it.
"You'd feel for coaches at the moment, because everything gets put on to game plans and stuff like that when you know, as a player, that's not the case. We have to be better with our execution, it's that simple."
O'Callaghan will be one of a number of changes made to the starting line-up for Sunday, with fellow internationals Peter O'Mahony, Simon Zebo and South African BJ Botha also set to start.
Flanker Tommy O'Donnell will earn his second Heineken Cup start. The Tipperary-born back-row made his European debut off the bench against Scarlets in 2011 and started for Munster in their quarter-final defeat to Ulster last season.
Munster will wait until the last moment before determining if Mike Sherry is fit to start. The hooker has been unable to train this week and has been wearing a compression boot in an effort to speed up his recovery.
If he is unable to start, his place will be taken by Damien Varley.