Brita filters only remove the smell of chlorine and i think some of the taste... it is my understanding that they don't actually take anything harmful out (just makes the tap water taste better for us humans). I am not 100% sure about that, so you will prob want to wait for a second opinion.
As far as using a Brita for tank water, I don't think you will see any benifit. An inexpensive temporary solution may be to try the tap water filter from Aquarium Pharmaceuticals (about $40.00 depending on where you buy it), it isn't the best but I belive it is better than nothing and prob a good temporary solution before you can purchase an RO/DI unit. The only problem is the replacement cartridges for the thing cost about $15.00 and only last a short while... so over time if you continue to use it you will have paid for your RO/DI unit and then some.
Cheers!