You can certainly drive a 4-digit multiplexed display at 20mA per segment with an AVR MCU (I'm thinking ATmega328P), if you don't have the constraints supercat mentioned and if you have 12 output pins to spare (7 for the segments, one for the colon, plus 4 more for multiplexing the digits). You will also be within the overal \$V_{cc}\$ or GND 200mA absolute maximum current for that MCU.
You can also use a BCD to 7-segment driver such as CD4011 (for common-cathode displays) or 74LS47 or 74LS247 (for common-anode displays) to save some pins and take the current load off of the MCU.
To save even more pins, you could use 8-bit shift registers such as the 74HC595. In this case you could use 2 shift registers: 7 pins for the segments, one for the colon, and 4 pins multiplexing the digits.