The team, who came into the tournament as the lowest-ranked team, have defied their fans' expectations by reaching the quarter-finals.
They have quickly been embraced as national heroes, with the mayor of Moscow responding by making additional public viewing space available in the city before the match in Sochi's Fisht Stadium.
"Now there is not so much pressure," midfielder Aleksandr Samedov told reporters. "Compared to before the tournament and the pressure we felt back then - it was much harder.
"Now we are in quarter-finals and we just want to bring pleasure to the supporters and to get further and we do not feel the pressure as we did before the tournament."
Accolades have included a bison being named after Russia's top striker Artem Dzyuba and a new-born eagle after goalkeeper Igor Akinfeev, who saved two penalties against 2010 World Cup winners Spain in the previous round.
Russia coach Stanislav Cherchesov knows that most of the 48,000-strong crowd will be supporting the home side but the moustachioed former goalkeeper has shown little interest in participating in the national outpouring of emotion.
"Emotions are simple. You show them when you direct the team. Now I am thinking only about the next game. These are not very sophisticated emotions," he said.
Cherchesov has several issues to resolve, with his midfield the biggest worry.
Alan Dzagoev has recovered from a hamstring injury but is still unable to take a full part in training while Samedov sat on the sidelines on Tuesday with an unspecified fitness problem.
Fellow midfielder Yuri Zhirkov has been ruled out injured and is unlikely to feature again, unless the hosts make it to the final in Moscow on July 15, according to Cherchesov.
The midfield is seen as a key battleground on Saturday, with Croatia's midfielder Luka Modric regarded as one of the best exponents in the world.
Stopping Modric's deliveries to a world-class attack that includes Mario Mandzukic, Ante Rebic, Marko Pjaca, Ivan Perisic and Andrej Kramaric will be crucial for the Russians.
They will have to attack Modric earlier than they managed to do against Spain's playmakers and will probably play a far more expansive game than last Sunday.
Russia have not reached a World Cup semi-final as an independent nation. The Soviet Union achieved the feat in 1966.
(Additional reporting by Maxim Rodionov; editing by Tony Lawrence)
