They are used to supporting their older products for years, look at Windows XP, there's been 3 generations of OS since XP and they are only now ditching support.
Consoles aren't OS's though. The people who keep things chugging along for a console in late generation are the new buyers and the core gamer (in this sense I mean core gamer in that they buy video games on a monthly basis and have a stack of about 40 games, or more, after a few years). Early and mid gen casual gamers (who only have a collection of 10 or fewer games by the time the generation gets to its later years) are not using their consoles enough to make continued support worthwhile. So MS will only continue to support XB360 as long as there's new buyers and the core doesn't jump straight on to Xb one.
The silver lining in the bad start Xb one PR had is that perhaps some of the core crowd will continue with Xb360 for a while, and for a year or two new buyers might decide to go with the 360.
This generation is different, but what is typically the next gen transition for the third placed console? I would think that the console that's selling best at the end of a generation (not necessarily the most LTD) has the best chance of continued sales well into the next generation.
All that said I think XB360 will be off the shelves after 3 Christmases post Xb one launch., so technically that means "years" and that makes the statement from MS true.
“The fundamental cause of the trouble is that in the modern world the stupid are cocksure while the intelligent are full of doubt.” - Bertrand Russell
"When the power of love overcomes the love of power, the world will know peace."
Jimi Hendrix
