It was revealed just this week that Wittke's driving licence was taken away from him for two months after he was caught on camera in November doing 109 kilometres per hour in a municipality where the speed limit was 50.
The transport minister and member of the conservative Christian Democrats (CDU) had apologized for his driving behaviour and promised to be more careful in the future.
But according to a Saturday article in the mass-market Bild newspaper, voices from various political camps are calling Wittke a bad example and saying he should step down.
"When a transport minister attracts that kind of attention, he doesn't just have a problem, he's got a big problem," said Dirk Fischer, the traffic expert of parliamentary group of Wittke's own CDU party. "In the end, he's supposed to be a guardian of the rules."
The vice chair of the Social Democrats in North Rhine-Westphalia, Jochen Ott, said that everyone is occasionally a little lead-footed in the car, but to get caught on a Friday morning at 8 a.m. at that speed is no small matter.
"Rather, it's irresponsible," he said. "A transport minister as inconsiderate speed demon – that kind of minister is no longer acceptable."
According to those close to the government in North Rhine-Westphalia, Premier Jürgen Rüttgers is not plan to fire Wittke, although the minister did have a "giant problem" on his hands and would be watched carefully.