AFAIK, the date time datatype stores data as timestamps. In order to accomplish what you're trying to do, I think you need to convert the first and last day of the month to timestamps, and then fetch objects where the date is higher than the first timestamp and lower than the second.
I have a similiar problem with the usage of attribute_filter. I want to get the next 5 items of my event content class from today on. I tested the following statement without success: