The Swans have made it through to the last eight of the FA Cup for the first time since 1964, although their passage through has been far from straightforward, as they needed replays to see off Wolves, Notts County and Sheffield Wednesday.
Next up for Carlos Carvalhal's side is a tough showdown with Premier League heavyweights Spurs and Abraham, who has netted twice during the Swans run to the last eight, knows his side will have to be on the top of their game if they are to make it through to the semi-finals.
"There is a chance to do something special in the cup this season but Tottenham are a fantastic team," Abraham told Swansea's official website. "We just have to go out and produce our A game - nothing less than that will do."
Swansea have a poor recent record against Spurs, as they have not beaten the North Londoners for nearly 27 years, while they have only claimed three draws from the fixture during their time in the Premier League.
However, one of those draws came at Wembley earlier this season and Abraham believes that stalemate can give his side belief ahead of Saturday's cup showdown.
The 20-year-old added: "Tottenham are a top-class team, but we earned a decent point against them at Wembley earlier this season."