Even talking about a 'fourth republic'.
France changed the number of republic many times.
Kaczyński wanted to change constitution and whole Poland (moraly- whatever he meant by this). The different number was meant to be a visible sign of significant change, just like in France.
Poles never really were convinced to change the number (even the supporters of Kaczyński brothers). The number of Polish republic changed only when the independence was restored: I Republic ended in 1795, the second Republic was restored in 1918 and the third in 1989.
As you can see the change in constitution would be a minor change in comparison to restoration of independence. Because of that the change of republic number was unjustified, so Poles didn't agree to that.
However the most ridiculous thing in this situation was that the changes in constitution was Kaczyński's political platform during presidential elections. He virtually can't do anything as president and still was proposing consitutional changes! Kaczyński's political platform was like Lord Farquaad castle;) Somebody had some kind of complex...