Mexican media called on Sven Goran-Eriksson to quit as national coach on Thursday, a day after his side lost to Honduras and avoided an early World Cup exit by the skin of their teeth.
Eriksson's team sneaked into the final stage of the CONCACAF zone qualifiers on goal difference ahead of Jamaica after Wednesday's embarrassing 1-0 defeat in San Pedro Sula.
Mexico, who had two players sent off, took only one point from three away games in semi-final Group Two, where they also suffered a humiliating defeat in Jamaica and were held 2-2 by Canada.
"Kick him out. It only costs $4 million (2 million pounds)," said the sports daily Record, referring to a penalty clause in Eriksson's contract if he is sacked.
"If they want, Record will pay the first dollar."
"We've qualified for the final stage but that's where the dreams of a country could go down the drain along with millions of dollars and a golden generation," added the newspaper.
The daily newspaper Reforma said Mexico had crawled through "despite their limited technique and the poor level of discipline."
Former England coach Eriksson replaced Hugo Sanchez who was fired after the under-23 team, which he also coached, failed to qualify for the Beijing Olympics.
Eriksson's appointment was controversial from the outset as critics questioned whether he was prepared for the idiosyncracies of Mexican football and the difficult conditions in Central America and the Caribbean.
Mexico goalkeeper Oswaldo Sanchez asked for more time for the Swedish coach.
"I give Eriksson my vote of confidence," he said. "The group is behind the coach. The defeat is sad but we progressed to the next stage."
The hiring and firing of the Mexico coach is decided by the presidents of the 18 first division clubs who are due to hold their next meeting in December.