The 60mA power requirement listed on page 13 of the om644p User Guide and Reference is more of an average consumption. The worst case could be more than 200mA depending on how hard you are driving I/O pins.
A better minimum consumption is 20mA. Of that 12mA is for the mega644p @14.7456MHz and 5V, 2-3mA for the power LED (which could be removed) and the rest for the MAX202 RS-232 level converter. There is not a powerdown facility on the MAX202. The SPI EEPROM does not use much power and could also be removed from its socket.
In order to operate the mega644p (or any microcontroller device) you also need to consider low power peripherals and various power sleep and shutdown modes. Section 9.11 on page 45 of the mega644 datasheet is a good place to start.
You can power the om644p all the way down to 2.7V and remain within specifications providing that you operate it at 10MHz or lower. If you want to use the om644p speed of 14.7456MHz then the minimum voltage should be 3.55V per the derating curve on page 329 of the mega644p datasheet.
The MAX202 is rated for 5V operation but seems to cope just fine with 2.7V. If you change the clock prescaler then you will need to also modify the Oak Micros bootloader frequency if you plan to use it.
I assume you meant inexpensive debugger. I use the "print line debugger" quite a bit and serves many needs. The Oak Micros boot loader, for example, was developed that way.
I understand the motivation for using a JTAG debugger but it comes at the cost of four I/O pins. Note that the om644 comes with JTAG disabled so that these four I/O pins can be used. You will need an ISP programmer to change these fuse bits.
The Atmel JTAG ICE mkII tool retails for $299 (Digikey). There are a number of clone debuggers (mostly based on the mkI interface) which you can find with Google. I do not have any experience with these and cannot recommend one way or another. You might try asking on
AVR Freaks.
Depending on your previous experience it might be best to start with the supplied bootloader and use simple print line debugging. Then as you get more familiar with tools and device you can proceed to getting an ISP programmer and then a JTAG debugger.