if its only for a 3V supply, then you really need to chop away at that sense resistor, 5V * 100mA = 0.5V, there goes your 2.7V turn on, though in truth, even a npn transistor will struggle a bit, you can possibly get as low at 50-100mV across the C-E junction with off the shelf transistors, leaving only another 100mV for the sense, so a 1 ohm or less resistor is ideal,