Is there a negative effect if I place an index on every column in a wide table?
It sounds like this is more of a DataWarehouse workload than an OLTP.
In that case, heavily indexed tables are normal. 

Keep in mind a couple of things, when you do your nightly loads, drop the indexes first then reindex after. Also, there will be a higher storage cost but generally this wont be a problem (but be aware of it).

I know your using 2008R2 but FYI, I believe the new columnstore indexes in 2012 shine against this type of workload. If you can't get the performance you want out of 2008R2 consider testing with this index technology on 2012.

Finally, you could monitor the index usage for the first few days/weeks There are missing index scripts and unused index scripts, that can be run on this table once the user query pattern is determined.