arusr:
I want to run a battery powered bread board Arduino on 3xAA batteries (so about 4.5V to 4.0V). I understand the concept of using a voltage divider to do level shifting between the ~4.5V MOSI pin on the Arduino to the radio module. But if your input voltage dips a bit, you won't get a consistent output voltage. I expect the battery voltage to drop over time, to from 4.5V to 4.0V before needing to change the batteries out.
It will actually drop a lot lower then 4.0V. AA batteries go from 1.6V (new) down to 1.0V (almost dead) so your voltage range from 3xAA is going to be 4.8V to 3.0V over the life of the battery.
arusr:
Is the voltage drop a big deal for radio modules like the RFM69?
Yes.
The simplest answer is to use a 5V voltage booster: 5v dc boost pfm for sale | eBay
Glue one of those to your 3xAA battery pack and connect your device to it with an old USB cable.