If you have an interest-only mortgage, then this incentive does indeed exist (assuming that interest-only loans are tax-deductible of course - I don't know what the situation is Stateside, but the UK no longer gives tax relief for any kind of mortgage interest). It's balanced by the need to have a chunk of ready cash available to pay off the principal at the point when the mortgage reaches term of course.
Regards Luke -- #include witty_sig.h
Over here, most mortgages are fixed payment for the entire term, typically 30 years. "Creative" mortgages have all sorts of variations, including several types where your payment can balloon up after a few years. These tend to be the ones that get people into trouble.