The Portuguese and their supremely talented squad are in real danger of missing out on a place in South Africa next summer - a defeat in Budapest would leave them six points adrift of even a play-off spot with just two games remaining.
Former Real Madrid boss Queiroz is confident Ronaldo and co can get a win against Hungary, however, which would see them draw level on points with their opponents. "We have to raise our heads and keep believing," said Queiroz. "The game is not over and while it lasts, we have to believe."
Hungary suffered a crushing blow to their qualification hopes when they conceded a last-minute winner to Sweden's Zlatan Ibrahimovic on Saturday. Speaking after the loss, Dutch coach Erwin Koeman admitted it may have left a psychological mark.
"The players will need a few days to digest this defeat," said Koeman, who is trying to guide Hungary to its first major international tournament since the 1986 FIFA World Cup in Mexico. "It's a huge disappointment for them."
Group leaders Denmark can move to within three points of qualification if they win in Albania. Morten Olsen's side drew 1-1 with Portugal in Copenhagen on Saturday, Sporting Lisbon striker Liedson grabbing a late equaliser for the visitors on his debut.
It was a result which Olsen described as "both satisfying and disappointing" but it still leaves his players in pole position. Matches in Tirana are rarely easy for visiting sides and the hosts have been hindered further by the news midfield powerhouse Lorik Cana will have to play at the back.
Tomorrow's other game sees the Swedes visit Malta. Sweden are currently third, five points behind Denmark and one adrift of Hungary. Coach Lars Lagerback should have Barcelona striker Ibrahimovic available after he shrugged off a knee injury to feature at the weekend.
Captain Gilbert Agius, Alex Muscat and goalkeeper Mario Muscat have been called back into the Malta squad. Coach John Buttigieg has made three changes to the 18-man party selected for Friday's 2-0 international friendly defeat to Cape Verde.