How early do I need to get to Marco Polo Airport for an early morning flight?

Is this a departure direct to North America, or to another European hub where you connect for the flight back to North America? I suspect it is the later, in which case it is just a "domestic" flight. If so, 1 1/2 hours should be sufficient. There are not many flights direct to North America from Venice any more, maybe a few in the summer. And those usually leave later in the morning.

Edit - Per your other post, I see you are connecting in Amsterdam.

Actually, the tickets we ended up with connect in Vienna. Austrian Air for all flights, although I think the Venice to Vienna leg may be one of their smaller partners. It sounds like arriving at 6:00 a.m. would give us enough time?

Ask your airline.
Different airlines have different rules for check-in times. Cheaper airlines require longer check-ins. And longer routes require longer check-ins.
The minimum check-in time should be stated either on the small print in your booking confirmation, and/or on the airline website.
Since you are changing planes in Vienna, you will not go through passport control at Venice airport. This will be done at Vienna because that is where you will be exiting the Schengen Area.

That early in the morning you will be okay on crowds.
We flew from Venice to Gatwick last April on a day when a couple of cruise ships were letting off cruisers. That Venice airport was packed with people and their 45 lb. humongous suitcases.
I have long since realized that second tier European airports have very early flights that take you to a big European gateway airport where you will sit until midday. Often, there will be another wave of flights going out at a more humane time--later in the morning. I try to stick to the later a.m. flights.

I had an early flight from Marco Polo last year. The place was a zoo with lots of people milling around. It took me at least half an hour to get oriented to the place and where I needed to go. I recommend 2 hours for the whole procedure.

But ask what time the airport opens! In 2012 we got there via hotel shuttle before all the lights were on, not pleasant for my not-a-morning-person body.