Proper Way of Powering a Circuit with 2 AA Batteries
Originally, all microcontrollers were designed to work off of 5v. Then 3.3v logic was introduced, and microcontrollers came out running off of that voltage.  Since then, those have been the two standard voltages, with 3.3v becoming the most popular.  Although many microcontrollers can go down to 2.7 or 2.6v or even lower, IMO it is best to run them off of 3.3v since a lot of peripherals are designed to do so also.
You want to use a boost regulator, like the MAX756 with an output of 3.3v at 300 mA.  It will take the AA batteries output, and keep the Vdd of the microcontroller constant at 3.3v as the batteries discharge.  It is available in single quantities for $5.43 at Digi-Key in an 8-pin DIP package.




Fresh AA batteries start out anywhere from 1.50v to 1.65v. which works out to 3.0v to 3.3v for two of them.  These means the battery voltage will never exceed the boost voltage of 3.3v.


As far as reading the battery voltage, since the Vdd of the microcontroller will be above the battery voltage, then you can feed the battery voltage directly into an analog input of your microcontroller and read it with the ADC.
If you are concerned you could put the batteries in backwards, then you can put a Schottky diode between the batteries and the input to the boost regulator.
As far as pullup resistors go, if the circuit is designed to ground the resistor with the button, as shown below, then there will be no current drawn when the switch is open.