Speaking at a press conference before Friday's protest, MSZP president Bertalan Toth alluded to possible protest action against businesses with ties to Orban's Fidesz party, as well as the big employers who stand to benefit from the overtime law.
The new law boosts the overtime employers can demand from 250 to 400 hours a year.
Some of the protesters are also angry at another law authorising new courts that they say could be politically manipulated.
MKKP launched more than a decade ago a way to poke fun at politics in Hungary, but it has now become a semi-serious force, using irony to tackle the most pressing situations in the central European nation.
MKKP's gathering started outside parliament late on Friday, where one protester brandished a placard saying "Happy boss, gloomy Sunday".
Edes was sceptical of any change being triggered by the rallies, but said he had joined to make his voice heard.
Mr Orban's Fidesz party has said protests are the work of foreign mercenaries paid by Hungarian-born United States billionaire George Soros.
He also repeated the government's accusation that the "most aggressive protesters are paid by George Soros", the liberal Hungarian-born U.S. billionaire and a frequent target of Orban's government. Irritating foreign schools will vanish. "And Soros, Soros, Soros, Soros, Soros", said an invitation to the rally posted on Facebook.
Demonstrators, subsequently joined by another rally called by opposition groups, then marched up to the presidential palace in Buda Castle, briefly blocking a bridge crossing the Danube River.
MKKP, which is not in parliament, had 3 percent support among voters in November according to pollsters Zavecz Research and Nezopont.
"I have come to rejoice over the government's policies", 28-year-old Gergo Gocza told Reuters, holding a sign saying "A Sign".
"This event is not meant to change anything", he said.
Orban insisted that "this law is a good law, we have to judge it on how it works in practice". Articles appear on euronews.com for a limited time.