Let me just say at the outset: the foundation for this rumor is incredibly shaky. Nintendo fan site Wii U Go (via Game Informer) has word from an alleged Electronic Arts insider that the publisher is "aggressively" working to make its Origin digital store the one that power's the Wii U console. Those talks have apparently extended to Steam owner Valve as well, but the biggest push is supposedly coming from EA.
Now, to put all of this in proper perspective, let's make it clear that the EA insider in this case is an intern who heard the information from a network engineer. This is about as far from the source as news can get. That said, it's an interesting possibility being raised here.
Let's face it: Nintendo doesn't have the best track record these days of keeping up with the needs of the so-called "hardcore" gamer. The Wii's lack of HD support continues to be a barrier for many serious gamers, something that the Wii U will most certainly try to correct. The thing that many industry observers note, however, is that the real battle in the next console generation will likely be waged online, in the social/community space.
Microsoft and Sony have done a considerable amount of work in this regard, but Nintendo's Friend Codes are seen as overly cumbersome and downright dated. The company has yet to detail any of the Wii U's online social features beyond vague mentions of leaving things to the third parties, but as things stand now, Nintendo is way behind in the online community race.
Having an existing service like Origin or Steam handle the console's online store also brings with it the added benefit of a built-in social network, as well as the community-building experience that Nintendo lacks.