how much power

Onemug,
Impedance being fairly flat is only one key to Maggies being an 'easy' load.
Second is line source. They couple very 'efficiently' into a room and don't drop level as rapidly as 'box' speakers of conventional design. The difference is not subtle
Third is phase. They don't have any of the wacky reactive behavior of some speakers which are at higher sensitivity.

Than again. some amps while measuring well into a resistor, do poorly with some types of reactive load.....be that capacitive or inductive.

To properly characterize a speaker as good/bad from the electrical load aspect, you need the phase data as well. Look up ANY of the stereophile speaker tests and they'll have such data. Any speaker with a big dip in impedance AND a high phase angle will be 'red flagged'. The warning will include advice to 'get thee a good amp'.

What is the minimum amout of current an amp has to deliver, to be considered a 'high current' amp?

Rok2id, the amount of specified current isn't important. A stability to the certain load is. An amplifier that delivers 60W onto 4Ohms presumed to have sufficient current to drive 4Ohm speakers.

Marakanetz:

my amp is rated at 150 wpc and 45 amps per channel. my speakers are 88db 4 ohm. Is this a good match? Smallish room and modertae levels, so I have no complaints, just curious.

Unless there is some very ugly quirk in the impedance curve/phase profile of the Vienna speakers, I'd find it hard to believe that the Denon's 125 wpc amp section will not comfortably drive them to levels well north of 75 db in an 11 x 15 room. As to available current and stability into the load, I seriously doubt that you have an issue with either.

It is certainly true that SQ may vary from power amp to power amp. Designs differ and different amps each interact in their own way with any given speaker's load, but that's a different kettle of fish. You may well prefer a different amp, but I highly doubt that you NEED one to drive your speakers to your desired levels.

Whatever else may be going on here, this set-up does not appear remotely underpowered to me.

Marty