The Black Cats have dragged themselves six points clear of the Barclays Premier League relegation zone with fine victories over Newcastle and Everton in their last two games, after a battling defeat at Chelsea, to hand new manager Paolo Di Canio a superb start to his reign.
One more win would take them to 40 points for the campaign and, particularly if it came at struggling Aston Villa on Monday evening, would virtually assure them of a place in next season's top flight.
However, such is the confidence currently flowing through the dressing room that O'Shea believes they can set out to win each of their remaining fixtures.
Asked how many points were still required, the 31-year-old defender said: "We will take another 12, to be honest.
"The next four games, the performances that we have shown, we are confident going into these matches.
"But first and foremost, we took the Chelsea step - we were unlucky we didn't get a point at least; we focused on Newcastle, we got the three; we focused on Everton, got the win, and we are just focusing on Villa.
"If we can get something down there, hopefully that should see us across (the line), but we have got two home games then against Stoke and Southampton and a tough away game, so the sooner the better, as they say."