The input sensitivity of the LM3886 is set by two resistors that determine the gain of the stage. So if the signal isn't enough I could always just increase the gain a bit. Normally people run these at somewhere between 15-30db gain (strangely enough if you make the gain TOO LOW the amp won't be stable!), but it can be set up for a bit more too.

From NS's excel spreadsheet design aid it looks like the lm3886 needs 1.150 volts rms to drive it to full output at 1% THD when set up for 26db gain.