Interim manager Benitez shrugged off the impact success or failure in Japan would have on his own short- and long-term job prospects, while goalkeeper Cech was happy with the favourites' tag that has been bestowed on the soon-to-be-deposed European champions.
Chelsea arrived in Yokohama on Sunday having given Benitez some breathing space with back-to-back victories following his nightmare start to life at Stamford Bridge.
The timing of Roberto Di Matteo's sacking as manager almost three weeks ago and Benitez's subsequent appointment until the end of the season appeared to be partly with success at the Club World Cup in mind.
The move threatened to backfire when Benitez failed to win any of his first three games in charge, but Chelsea departed for the Far East on Saturday night on the back of a much-needed confidence boost.
They must now build on that to avoid surrendering a fourth piece of silverware already this season, something that would do no good at all to Benitez's hopes of remaining at Stamford Bridge or landing another big job.
The former Liverpool boss told a press conference: "With the economic crisis around the world, everybody is under pressure.
"I don't have a problem with pressure. The future is the next game and the one after that."
That next game is Thursday's semi-final against CONCACAF champions Monterrey, followed by either the final or third-placed play-off against South American champions Corinthians or Egypt's Al-Ahly on Sunday.
Benitez said of the Club World Cup, which he won with Inter Milan in 2010 after losing the 2005 final with Liverpool: "It's a massive competition. Everybody here has the same idea as me - to win every trophy."