VW CEO Matthias Mueller spoke to journalists in Detroit last week. Image source: Volkswagen.

New Volkswagen (NASDAQOTH:VWAGY) CEO Matthias Mueller drew sharp criticism after what seemed like a tone-deaf interview in the U.S. last week. 

But he apparently isn't in danger of losing his job, at least not yet. A VW spokesperson told Bloomberg that the company's supervisory board strongly supported Mueller after meeting with him earlier this week.

It's not a surprise, but even VW's board must be concerned about the growing pressure on the German auto giant.

Following up a tough week for the CEO in the U.S.
Mueller didn't win over a lot of new friends in his first trip to the U.S. since taking the top job at the German auto giant last week.

After some tone-deaf remarks at a media gathering, he stumbled so badly in an interview with NPR, seeming to deny that VW deliberately broke U.S. laws, that the company's PR mavens asked the network for a do-over.

The do-over was granted, and it went somewhat better. But it served to emphasize that four months after the U.S. Environmental Protection Agency (EPA) first charged VW with years of cheating on emissions tests, the company is in many ways still figuring out how to respond. 

VW has admitted to selling about 11 million diesel-powered vehicles around the world that were equipped with what the EPA deems to be a "defeat device," software that turned on parts of the cars' emissions-control systems only when it detected that a government emissions test was under way. In normal driving, the cars emit toxic pollutants at a much higher level than is allowed under the laws of many countries, including the U.S.

VW has started recalling the affected vehicles in Europe. But U.S. regulators, operating under the stricter standards of the U.S. Clean Air Act, rejected the company's plan to fix the roughly 500,000 affected vehicles in the U.S. It is believed that the EPA and California regulators are pressuring VW to buy back some or all of the cars, a move that could cost several billion dollars. 

Mueller has made some big changes, but VW is losing ground
Mueller hasn't sat idle since taking over the top job shortly after the scandal broke. He has shaken up VW's executive suite, revamped the company's product-development process, and commissioned an extensive investigation in an attempt to find out who and what was responsible for creating the software that has put the company in crisis. A report on that investigation is expected at the company's annual shareholder meeting in April. 

In December, VW hired Kenneth Feinberg, the attorney who ran a compensation fund for victims of General Motors' (NYSE:GM) defective ignition switches, to manage a similar program for owners of the affected VW vehicles. But so far, it's unclear exactly what the fund will cover, or who will be able to make a claim.

Meanwhile, VW's sales have taken a hit, and not just in the United States. After years of pushing to be the world's largest automaker, the company's global sales declined to 9.93 million vehicles in 2015 from 10.14 million in 2014, almost certainly leaving giant Toyota (NYSE:TM) as the world's largest-selling automaker for yet another year. (Toyota will report its full-year global sales on February 5.) 

More worrisome for VW shareholders, the company lost its leadership in the huge and important Chinese market. VW's sales in China fell 3.4% to 3.55 million vehicles in 2015, while longtime regional arch-rival GM's rose 5.2% to 3.61 million.

The big challenge that Mueller needs to solve -- soon
Mueller has a lot of challenges on his plate. But perhaps the most acute one is the need to make peace with U.S. regulators. Mueller had a closed-door meeting with EPA chief Gina McCarthy in Washington last week, but it's unclear what -- if anything -- was settled in that discussion.

The road to getting VW past the scandal starts with the EPA. How Mueller solves that puzzle will tell us a lot about VW's prospects going forward.