Does being an 'otaku' imply something negative in Japanese?Yes it does.
They are usually seen as socially withdrawn nerds at best, or mentally disturbed criminals-to-be at worst.
Illustrative example: Akihabara (or 'Akiba' in short)
This is a district of Tokyo and the mekka of 2D-subculture in Japan. There are a few leftover consumer electronics shops in there, but most of the streets are crammed with shops selling anime, manga and adult games, including tons of related merchandise. The streets are swarming with teenage Otaku, maids and cosplayers, especially on weekends.
It's a pretty nice and colorful place actually, but in the eyes of the general public, it has a seriously shady reputation that is quite representative of the image of Otaku in general. Depending on who you ask it is considered either "just suspicious" or outright dangerous. It's a place where most people wouldn't let their teenage daughter go alone, for example.
There are some efforts to turn it into a foreign tourist attraction (some banners flying the "Youkoso Japan" logo from every streetlights there, among other things), but like many of these initiatives directed at foreigners in Japan, the budget seems to be rather limited.
That being said, it is worth mentioning that the overall status of Otaku briefly improved during and after the airing of the Densha Otoko drama series in 2005-2007. It was a brief fad when Otaku had not much of negative reputation, but it did not last long.
By and large the media coverage seems to have returned to only mentioning them in negative contexts again. One thing that especially keeps popping up when talking to Japanese people about Otaku or Akihabara these days, is the 2008 incident that occured in Akihabara when some deranged person (who was allegedly an Otaku or Hikkikomori) drove a truck into a crowd, trying to indiscriminately kill people.
Generally speaking, whatever meaning the term "Otaku" may carry in the West these days: When talking to Japanese acquaintances, it's fine to mention that you enjoy the 2D-subculture like anime or manga (as that in itself does not carry much of a stigma), but I would advise against calling yourself an "Otaku". At least unless the person on the other side already knows you well.