Is it possible to design a digital filter that rejects 60Hz noise while keeping step response in the time domain below one mili-second
You can trade off steepness of the notch against time domain ringing. That's a fundamental trade off and there is no way around it. When using an IIR notch you can simply adjust the "Q" (quality factor). A Q of 3 will give a step response that's roughly 10ms long.