That is an excellent question. The amp chip itself is the LM3886. I know the output impedance as an audio amp is best at 4 or 8 ohms. THe input impedance, hmm, I just went through the datasheet but that number eluded me. There seemed to be a reference to 10K but I didn't quite understand it. The datasheet shows Rin as a potentiometer with a value of 10K then a series 1K resistor going to the input.
Then I would think a 10k pot would work for your requirement. You might want to add a resistor in series with the 555 output to the pot to limit the maximum voltage to the amp.
I found a post on this forum which noted the output of a 555 at 7.7Vpp. I checked a datasheet and it was noted at 10Vpp, but I'm not completely adept at reading datasheets. If the output is 7.7Vpp would the 10K pot allow me to input 0-2Vpp?