A survey showed 62 percent of those polled by peil.nl expect the Netherlands to win after their 3-0 defeat of Latvia on Wednesday helped secure a place in the last eight.
Dutch politicians are among those to have expressed support for Advocaat, slammed after a 3-2 defeat by the Czech Republic followed his controversial substitution of winger Arjen Robben.
Ministers criticised a call by a television commentator after that game for Advocaat to be stoned and hanged, saying they were afraid viewers might take such comments seriously.
"Such abuse goes absolutely too far," Interior Minister Johan Remkes was quoted as saying in the Algemeen Dagblad.
A new website offers fans T-shirts to show their real feelings for the coach: "Our Dick has balls", "Our Dick never gives up", "Our Dick will always score", "Our Dick is 1.69 m tall" are some of the slogans to choose from.
Dutch supporters have deluged the Czech embassy with messages of thanks and flowers after the Czechs' 2-1 defeat of Germany ensured the Dutch a quarter-final place.
A website set up to thank the Czech "saviours of Orange" has registered almost 75,000 Dutch thank-you.
