Martin Winterkorn, the head of Volkswagen, said his company plans to storm the North American market with a $7 billion investment. So far, the German car manufacturer has made almost no advances in the United States. Its market share in December was 2.5%, a sign its sales continued to erode.

Based on the market shares of other manufacturers in America, and VW’s aspirations, what Winterkorn means is that his company can take part of the market from General Motors Co. (NYSE: GM), Ford Motor Co. (NYSE: F) and Toyota Motor Corp. (NYSE: TM). Among them, they have a market share of more than 48%, as well as tremendously large model lines. No company can increase sales by much in America, outside the luxury segment, without taking sales away from these three.

VW’s car line is such that its target is the middle of the market, which is the largest and most competitive. With the exception of its expensive Touareg SUV, VW’s models carry prices between $16,000 and $35,000. GM, Ford and Toyota have dozens of vehicles with similar features and prices. Additionally, every other manufacture of any size has set its aim on the same portion of the market. The second-tier manufacturers in U.S. sales — Chrysler, Honda Motor Co. Ltd. (NYSE: HMC) and Nissan — each has an armada of cars and light trucks targeted in the same direction as well.

VW’s greatest Achilles’ heel, beyond its modest line-up, has been the consumer’s perception of its quality. Buyers watch measures from research firms J.D. Power and Consumer Reports carefully. And VW has faltered in results for quality. Even if the workmanship on its cars improves, it may take several years for the effects of that to reach the buying public.

GM, Ford and Toyota hold several other advantages. Each has hundreds of dealers, most of which have sold their cars for decades. Each has marketing budgets that run well into the tens of millions of dollars. Perhaps ahead of anything else, each has millions of customers. The most successful manufacturers are those that have buyers who return again and again to buy new cars. VW has to contend with nearly 50% of the market among the Big Three, and many of their customers have no intention of turning elsewhere for new cars.

VW’s challenge may not be impossible, but it is close.

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