I have been able to use it (USBasp V2.0 Lcsoft Studio) with Arduino IDE 1.0.3 and with the ATtiny cores. I have tested it successfully with programming an ATtiny85 at 8MHz and ATtiny13A running at 128Khz clock.
One thing to note with any USBasp working with the Arduino IDE, there is a limitation that the IDE is not able to select a slow clk option with the USBasp programmers. So I did have to jumper JP3 on the USBasp board to force the slow clk option to program the ATtiny13A running at 128KHz.
If you don't use the IDE and use avrdude from command line then you can use the -B 50 option to slow the programmer down. But this only will work if the programmer is using the fischl.de firmware 2009 or 2011. The older firmwares did not support this option.