Honestly, the biggest hinderance is going to be kanji. The Japanese government has defined a set of a bit over 2000 kanji as a set called the Joyo Kanji, which is the list of kanji which may be used in official documents and newspapers and the like. Fortunately, like many things, the Joyo Kanji obey the old 80-20 rule – the 20% most-used kanji make up about 80% of what you’re going to encounter in the wild, which means that with 400 kanji under your belt, you’ll probably be able to read most things. Once you learn 1000 kanji, that percentage goes up to 95% or even 99%.
Fortunately, TextFugu includes 412 kanji in its lessons. However, Koichi doesn’t teach the kanji by order of frequency, so you may find yourself lacking in some areas. So by the time you finish the lessons here, you might be able to read a newspaper, though you’ll almost certainly have to look up technical terms.
Not trying to get you down, just letting you know what you’re in for.
Also, vocab may be an issue. You may find yourself requring the aid of a dictionary.
It’s possible to do, though. I bought δΊγε½ for the DS a while back, and I was surprised by how easily I could read everything. Mind you, all the kanji has furigana, so that helps.
After all that, your best bet is probably just to give it a stab and see what happens. A good place to start might be http://www.asagaku.com/ – it’s a version of the Asahi Shimbun daily newspaper designed for school students.