Statistically speaking, highly unlikely!
Because of the 55 times India has been set a target of 275 or more in a 50 over match, they have lost 46 times and won only 8 times (one was a no result). A Win/Lose ratio of 0.174 does not look promising!
Against New Zealand, they have only won once chasing more than 275 (in 1988/89 at Vadodora chasing 281) and lost 3 times (1995/96 Nagpur, 1998/99 Christchurch and 1999/00 Rajkot).
And to make it worse, they have won only once chasing the 275+outside the sub-continent (against england in the famous 2002 Natwest finals) .
And if 270+ seems too much, here is some more stats regarding run chases:
Chasing 250+, won 25, Lost 83.
Chasing 260+, won 18, Lost 65.
If I were a betting man, I would bet on India losing this game. But they say, cricket is a funny old game....