Yes, the USBASP V2.0 LCsoft Studio usually supports sck auto-clock adjust for AVRs running down to 1MHz. That USBasp firmware can be upgraded to support lower speeds for AVRs running at 128KHz. In addition it does have the hardware jumper (J3) support for slow sck clock, but only if you update the firmware. I have one of those USBasp programmers and have tried this, so I know it works. But I think you have a bigger problem with your fuse selection.
Are you saying you programmed the low fuse byte with 0xF8? If so then yes, you will need to connect an external ceramic resonator (not a crystal according to the datasheet) in the range from 400KHz - 900KHz.
The low byte fuse setting for the internal 8MHz clock should have been something like 0xE2.