narcoleptic library doesn't compile with Mega2560 or 1284p

Power-down mode is the deepest sleep mode, in which the MCU will only draw about 0.1µA. The watchdog timer (WDT) can be used to wake it. The WDT requires 4-5µA to run, which is still hardly anything. The watchdog is not terribly accurate, so if you want something very close to 20 sec, some calibration may be needed, which will be specific to each individual MCU chip. The watchdog is also not infinitely variable, it can generate interrupts (to wake the MCU) at roughly 8, 4, 2, 1 seconds, or at 500, 250, 125, 64, 32, 16ms. It's common to sleep for several WDT periods to effectively generate longer periods; this technique should add virtually nothing to power consumption. An external RTC can be used to generate interrupts more accurately at specified times but it doesn't sound like that's part of the plans.