Their worry, however, is that the strict disciplinarian's zero-tolerance policy might ultimately weaken, not strengthen, their bid for glory.
Smuda, who took the post in 2009 after their failure to qualify for the World Cup in South Africa, has already banned some high-profile players from the squad over alcohol-related incidents, including goalkeeper Artur Boruc.
Most recently, he dropped Slawomir Peszko and Marcin Wasilewski after a night out that ended with the former in police custody, though Wasilewski has made the squad for Euro 2012.
Some critics feel the coach could end up hurting Poland's chances in front of their home crowd by taking his anti-alcohol crusade too far. Others believe he must defend his authority by allowing no exceptions.
Smuda's disciplinarian ways, which have their roots in his time coaching in Germany's lower leagues, helped him lead Widzew Lodz to two league titles and the Champions League quarter-finals in 1996.
That was the last significant Champions League appearance by a Polish team and Smuda then won another Polish championship with Wisla Krakow.
Smuda was born in 1948 in a village in Poland's southern Silesia region with strong historic links to Germany and has spent a large part of his life abroad - both factors may help explain why he can often appear at odds with the Polish language.
His foreign experiences have not all been happy. Smuda lost his life savings to a dishonest businessman along with Kazimierz Deyna, perhaps Poland's greatest footballer of all time, when the two were trying to settle in the United States in 1970s.
He subsequently spent time playing in the old NASL (North American Soccer League) for Hartford Bi-Centennials, the Oakland Stompers and the Los Angeles Aztecs among others and while in LA played alongside the flamboyant, brilliant George Best.
It would be hard to imagine two team-mates so dissimilar.
As Poland coach, he has earned a reputation for filling his squad with foreign-born players with Polish roots. One prime example is the French-born Damien Perquis, who was granted Polish citizenship.
Other players who were born in Poland but have spent most of their lives and developed their careers abroad also entered the fold, namely Eugen Polanski, Sebastian Boenisch and Adam Matuszczyk.
Smuda's record in friendlies ahead of the tournament has been mixed, though and he has repeatedly said he will quit after the tournament if Poland miss this rare opportunity to make an impact in the international arena.
The Poles last reached the latter stages of a major tournament in 1986, yet a top-two finish in a group containing Russia, Greece and the Czech Republic is seen as the absolute minimum requirement.
If he really quits, it seems possible Smuda may pursue his dream of returning to his German coaching roots, albeit this time in the Bundesliga.