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."
Chelsea's hopes have been further boosted by the return to form of Fernando Torres but Benitez played down his own contribution to his fellow Spaniard's four goals in two matches.
He said: "The manager can communicate with the players, yes, but when a player is in good form it's largely because of his team-mates."
Europe has won the last five Club World Cups and a resurgent Chelsea will be expected to make it six in a row for the continent.
Cech, who has been captaining the side in the absence of the injured John Terry and Frank Lampard, said: "We were already straight into the semi-finals, like Corinthians, so we have to be seen as the favourites.
"I can live with that fact. It's not a problem for us. We came to do our best and try to win the competition, and we can assume the position of favourites and will try to prove this on the pitch."
The Club World Cup has been derided by some as an unwanted distraction for European teams, with the Champions League still seen as the ultimate prize.
But Cech said: "I'm actually very happy that we can be here for this tournament. It means a lot to every player to play in great tournaments.
"You only get the invitation to play here if you win the Champions League, and that's not easy to achieve. It took me eight years at Chelsea to get the invitation to play in this tournament.
"We hope we make the most of it and win. The last two results were very good for us, so we will try to carry on with this momentum and that can take us through."
Lampard could return to lead Chelsea in Thursday's game but Terry was left in London due to the risk of aggravating his knee injury.
Oriol Romeu (knee) and Daniel Sturridge (hamstring) could yet fly out to join a squad which trained for the first time in Yokohama today as they attempted to acclimatise to the conditions and time difference.
Cech claimed Monterrey had an "advantage" on that front as they had already beaten South Korean club Ulsan Hyundai in Sunday's quarter-final.
The 30-year-old did welcome one particular change that will greet Chelsea on Thursday, the use of goalline technology at the tournament.
The International Stadium in Yokohama will employ the magnetic field-based GoalRef system.
"I'm very happy with the decision that technology goes forward," Cech said, glancing at Benitez in apparent recognition of Liverpool's famous 'ghost goal' against Chelsea in 2005.
"I've been saying for the past 10 years that it was a big fact that football needed this.
"You can see in the course of history that results in certain competitions could've been different."
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