Working Remotely in the U.S. While In Spain

I have a remote position where my employers don't care where I work or even what time zone I'm in. 

Would it be possible for me to get a visa to live in Spain for a year or possibly two while working for my U.S. company?

I understand that I would have to file taxes in both the US and Spain and that the tax agreement keeps me from paying double. 

But is my remote income a concern for getting a Visa? Seems like Spain shouldn't care as long as I'm not taking a job away from a Spaniard.