Alcorcon, from Segunda B (the third tier of Spanish football), stunned the nine-times European champions in the first leg two weeks ago, in a result that raised questions over the future of coach Manuel Pellegrini.
However, Real's reaction since then has quelled talk of a crisis and two wins and a draw in all competitions have given them confidence they can see off a side with a budget 400 times smaller than their own.
"For pride and for the history of Real Madrid, we have to win this tie," Brazil's Kaka told the club website.
"The players and the fans have to stand together. The Bernabeu must be a wave of pressure."
Pellegrini will be unable to draw on the injured Cristiano Ronaldo and suspended Sergio Ramos but Alcorcon coach Juan Antonio Anquela was keeping his feet on the ground.
"We are optimistic but realistic. If Real Madrid perform to their usual standards our chances of progressing are minimal," he told sports daily Marca on Monday.
UNDER PRESSURE
Other top-flight sides battling to stay in the competition against lower-league opposition are Tenerife, Racing Santander, Almeria and last year's finalists Athletic Bilbao, who all lost their first legs.
The 23-times Cup winners Bilbao trail second division Rayo Vallecano 2-0 but have home advantage on Wednesday.
The Basques hope to have Spain striker Fernando Llorente back from injury in time for the game.
Racing are 1-0 down against second division Salamanca on Wednesday and a run of eight matches without a win in all competitions has coach Juan Carlos Mandia under pressure to turn things round.
"I expect to be coaching Racing for many weeks to come and I won't give up," Mandia responded when asked about his future after his side's 2-0 home league defeat to Bilbao on Sunday.
Misfiring Atletico Madrid have a 2-0 lead over Segunda B side Marbella on Tuesday, while fellow la Liga strugglers Villarreal are level at 1-1 for the visit of Segunda B's Puertollano on Tuesday.
Holders and la Liga leaders Barcelona have a 2-0 lead going into their clash with Segunda B's Cultural Leonesa at the Nou Camp on Tuesday.
