The Black Cats remain six points clear of the Barclays Premier League basement battle despite having taken a paltry two points from their last six games.
However, Sunday's clash with Norwich, who are three points better off, signals the end of a sequence of fixtures against sides in the lower reaches of the table and heralds the onset of a run of games which will see them face Manchester United, Chelsea and Everton either side of a derby trip to fast-improving Newcastle.
In the circumstances, victory over Norwich would go a long way towards easing their fears of being sucked into the mire below with last weekend's conquerors QPR and Aston Villa in particular starting to rally.
Asked if that piled the pressure on Sunderland's shoulders, 31-year-old O'Shea said: "As professionals, it shouldn't do. Why should it?
"There are 90 minutes in a game of football - if it's 0-0 in the 75th minute, there's no problem.
"We are more than capable of scoring goals in the last 10 minutes as well as the first 10 minutes.
"It's going to be important on Sunday that the players stand up with bravery and composure and the attitude to come and take the ball, come and want to play, want to play football and not hide and shy away from the challenges that we face."
Should the Black Cats fail to collect the three points on offer this weekend, they would be left looking uneasily over their shoulders and with a daunting series of matches ahead of them.
However, just as O'Shea will take nothing for granted against Norwich, he refuses to accept that the Black Cats should write of the possibility of emerging from their clashes with United, Chelsea, Newcastle and Everton empty-handed.
He said: "That's one of those things. If the Premier League worked like that, everyone would have their points worked out before the start of the season and we could all pack up and go on our holidays.
"It never works like that in the Premier League, we have clearly seen that in the last few weeks - never mind the last few weeks, since the Premier League started.
"Everyone likes to predict they can take points here or take points there, but it never works like that.
"Every game has its own individual facts and bases to go from and that's what we will be doing on Sunday, and then you deal with one game at a time."
Given the importance of Sunday's game, Martin O'Neill and his players could be forgiven for approaching it as if it were a cup final.
However, Republic of Ireland international O'Shea, who has spent most of his career at the other end of the table, is experienced enough to know that nothing will be decided this weekend.
He said: "It's a very big game, don't get me wrong, but the season doesn't finish after Sunday.
"We are not under-estimating the fact that it's a big game - believe me, we know that - but there are lots of big games after to come as well."
O'Shea admits until Sunderland manage to ease themselves clear of the developing scramble at the foot of the table, there will be a concern over their status, but he remains confident that they have the wherewithal to do just that.
He said: "There's always been a worry, ever since you don't get yourself up to that comfortable position in the table. I don't think we have ever tried to hide the fact here at Sunderland.
"We know that we have been close to the top 10, but we have also been close to the bottom three, so it's never been hidden, that fact, it's always been there bang smack in front of us."