It depends on what you're looking forward to from your trip. The North and South are diverse in them selves so why don't you split up 3 weeks for south and 3 weeks for north ? I'm sure you wouldn't be disappointed if you've never been here in India. It'd be a little chaotic and weird for you Americans but it's the same for even us Indians. So you're welcome to fly in and find out. BTW I'm from southern state of India, Kerala, which is known by the name Gods Own Country. :)

best varun