There is no reason why you would not be able to learn kanji. It undoubtedly seems daunting right now, but remember the old joke about how you eat an elephant (one bite at a time).
The new JLPT is split into five levels, N5 (lowest) to N1 (highest). You don't have to take them in order, and many people skip the lower levels. They can be a useful target - but it depends what your aims are. They don't test writing or speaking abilities, either.
Erin's Challenge is a useful site for beginners or "false-beginners" (e.g. if you've had some classes and want to review).
Coscom have some kanji material (some free/online, some not). Generally I recommend material that shows you the kanji in some sort of context (e.g. with words/sentences showing how it is used), because the readings and meanings of some kanji change depending on how they're used.
e.g. 着 is a common kanji that sometimes means "wear" (like clothing - it's the "ki" in "kimono"), and sometimes means "arrive/arrival". 手 (て - hand) is found in the word for singer (歌手 - かしゅ) because when it comes at the end of a word it sometimes means "person who does X". On the other hand, 駅 (えき - station) is consistent (always read the same, always means the same).
There are also lots of patterns. 海、湖、潮、液 all have the same three strokes on the left hand side (氵) - that is a radical called "さんずい" or "three drops", and the kanji that have it usually mean something to do with water or fluid.
If you take one and break it up, 湖 (lake) is made up of 氵+古 (old)+月 (moon) - if the latter two don't seem to have too much to do with the meaning of lake, it's because the 胡 part is about the sound. 古、胡、 and 湖 can all be read こ (on-reading, often used in kanji compounds). Many kanji are made up like this - a meaning part, and a sound part.