The 21-year-old, who was a surprise inclusion in Vicente del Bosque's squad and has made only three appearances for the European champions, will almost certainly fill the holding midfield role alongside Sergio Busquets if Alonso is ruled out.
"I hope that Xabi recovers as he is a key part of the team," Martinez told a news conference at Spain's training base on Sunday.
"But if I get my turn then I am totally prepared. It's a responsibility but I will do everything in my power to try and do the job well."
Losing the experienced Alonso, who damaged the ankle in Friday's 2-1 win over Chile, would be a major blow to the pre-tournament favourites against a Portugal side that did not concede a single goal during the group stage.
However, Del Bosque said on Saturday he had full confidence in Martinez, who replaced Alonso in the 73rd minute against Chile, and predicted the Athletic Bilbao player had a long international career ahead of him.
Spain will also have to contend on Tuesday with Portugal's Cristiano Ronaldo, who plays with Alonso, Iker Casillas, Sergio Ramos, Raul Albiol and Alvaro Arbeloa at Real Madrid.
Forward Juan Mata told Sunday's news conference there was more to the Portuguese than the former World Player of the Year.
"They are a very compact unit, defensively very strong but also with a great deal of penetration," he said.
The winners of the match at Cape Town's Green Point Stadium will progress to a quarter-final against Paraguay or Japan.
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