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The pressure on Volkswagen (NASDAQOTH:VLKAY) is increasing: The company's second-largest shareholder said Monday that the company has to come clean on its diesel-cheating scandal within three months -- or else.

What's happening
Stephan Weil is the prime minister of Lower Saxony, the second-largest of Germany's 16 states. His position and influence is comparable to that of a governor of a large U.S. state. The state of Lower Saxony is VW's second-largest shareholder, and it wields considerable clout inside the company.

In other words, Weil isn't just some politician grandstanding. He's someone VW CEO Matthias Mueller is obliged to heed. 

Weil said in an interview on Monday that "there is a very legitimate concern on the part of U.S. authorities, the public, and the company itself for a comprehensive investigation," according to a Bloomberg report. He demanded a "complete clarification" from VW within three months.

That timeline probably wasn't chosen out of thin air. VW has hired U.S. law firm Jones Day to conduct an investigation into the events that led engineers to incorporate an emissions "defeat device" into millions of diesel-powered VW and Audi vehicles. Mueller has said VW will provide a report on that investigation at its annual shareholders' meeting on April 21 -- or in about three months.

I think the real message Weil intended to deliver is that the report in April had better be the whole story.

VW's response so far hasn't been convincing
Since the U.S. Environmental Protection Agency (EPA) made public its allegations against VW in September, the company has maintained that the cheating was the work of a few engineers acting on their own, in secret. Mueller, who took over after former CEO Martin Winterkorn left a few days after the EPA's announcement, has promised complete openness. 

But so far, the company's response to the scandal appears less than convincing. A few top engineers were "suspended" last fall, meaning they were sent home with pay.

But beyond that, little appears to have changed at VW. Mueller came under fire earlier this month after suggesting in Detroit that the whole thing might have been a misunderstanding. 

But worse than any individual's remarks, VW is giving the impression that it doesn't really take the scandal all that seriously. Maybe worse, it doesn't yet appear to be determined to make the changes necessary to avoid such problems in the future. 

VW's needs to look to these examples -- now
Weil appears to recognize what most observers outside of Germany have been saying: The longer VW drags this out, the greater the long-term damage to the company. 

A few years ago, when Toyota (NYSE:TM) was caught in a scandal over "sudden acceleration," the company at first appeared to be playing for time, concealing data and denying culpability. But eventually, CEO Akio Toyoda came to the United States and made a humbling appearance before Congress, taking responsibility for the events and promising to make changes at Toyota. 

And then, importantly, he delivered on those promises. 

Likewise, when a potentially devastating scandal over defective ignition switches erupted just a few weeks into new General Motors (NYSE:GM) CEO Mary Barra's tenure, she mustered a convincing response fairly quickly. The company issued apologies and quickly paid a hefty fine without argument, Barra appeared before Congress on two occasions, a fund was established to compensate victims of accidents that happened before GM's bankruptcy, and she ordered the recall of millions of GM vehicles in an effort to take care of any other lingering problems before they blew up.

Those were convincing responses to potentially devastating scandals. Toyota's reputation (and sales) have since fully recovered, and GM -- despite lingering litigation related to the scandal -- appears to be moving past it quite well. 

The damage is already spreading
After Mueller's first press conference in December, I was optimistic he would be able to muster a similarly convincing response from VW. But it hasn't appeared yet, and VW's sales are slipping around the world.

The longer VW waits to come clean and make amends, the longer it will take for the company to recover its reputation and customers. For anyone considering an investment in beaten-up VW shares, the response of the company to the scandal so far has to give pause. 

John Rosevear owns shares of General Motors. The Motley Fool recommends General Motors. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.