The Portuguese -- finalists in 2004 when they hosted the tournament -- opened their Euro 2012 campaign with a far from dishonourable 1-0 defeat to the hands of one of the favourites for the title, Germany.
But with the Danes, champions in 1992, having stunned the Dutch, Paulo Bento's team know that while a draw would at least give them an outside chance of reaching the last eight, nothing short of victory is required with the Dutch still to play.
Portugal, though, face an uphill battle, with the Danes on the up and having beaten the Selecao 2-1 in the final tournament qualifier in Copenhagen last October, making it three wins from five against the Portuguese, and forcing them to play-off. Pivotal to them getting something out of the game will be for their captain and one world class player Cristiano Ronaldo to get more involved than he was after yet another disappointing performance for him at this level against the Germans.
In his defence, the 26-year-old Real Madrid superstar does not have the same quality of playing talent supporting him as he had when he first made an impression as a player in the 2004 tournament.
Indeed, one of those players of the so-called "golden generation" of Portuguese players, Luis Figo, sprang to his defence on Sunday and called on Ronaldo's team-mates to give him the opportunity to display his considerable talents.
"I think the team need to give him the chances to have a good performance," said the 39-year-old former Real Madrid star. "The characteristic of Cristiano is to finish, to score, so, if the team don't produce those kind of opportunities then of course his performance is down."