Looking historically Mario Kart have recently had pretty nice debuts, so i'd say:

FW in all territories: 1 100 000

I dont know when it will release, but say it release in April to great reviews and a great marketing campaign:

6 200 000

Lifetime if WiiU starts gaining a little momentum:

11 000 000

First Week - 450k
2014 - 4,5mil
LT - 8mil

First Week: 475k
2014: 4 million
Lifetime: 12 million

Well, somebody has got to go against the grain.

30 million LT.

First week: 420,000
2014: 3.3 million
Lifetime: 8.75 million

First Week 210K
2014 2.6 million
LT 6.1 million

first week: 312 k
2014:3.29 m
lifetime:6.43 m

Mario Kart 8 to outsell the Wii U confirmed.

300K for the first week.
2.5 million first year.
6 million lifetime.

EDIT: Shit, I forgot it's coming out in Spring. Numbers changed.

Don't forget about all those people who don't realize that Wii U is not a Wii peripheral.