I frequently have LEDs + current limiting resistors connected to ISP pins. The current consumption is a bit south of 16 ma.
Commercial programmers (like the Pololu AVR Programmer) sometimes have series resistors on the ISP lines. I guess the series resistors plus an LED and resistor may cause problems (it has never caused problems for me).
A piezoelectric buzzer has caused problems for me (Teensy was the programmer). Adding a small value resistor (22 ohms) eliminated the problem.