AVRDUDE throws "target doesn't answer." with USBASP and ATMEGA48PA
You can fuse off the Atmega48's ISP interface if you corrupt the incoming programming data stream just-so, but it would be very difficult to do. Although, I've seen it happen with shifted byte streams which your manual override of the reset line could have caused (but still highly unlikely).

It's also possible that the USBASP needs a firmware update (as suggested by the warning message) or merely needs to be re-flashed. As in, you just got unlucky with your timing and really this is an unrelated failure in the USPASP.

avrdude is awful at debugging programming communication problems. You are better off using AVR Programmer (part of AVR Studio) for this.

For the general diagnostic procedure, see this question:

avrispMKII short circuit protection triggering when programming