Too busy to chant sixteen rounds
Srila Prabhupada gave a clue how a busy man in household life might chant sixteen rounds: chant four before breakfast, four before lunch, four before dinner, and four before taking rest for the evening.
Another point is that since chanting elevates our consciousness, whose who chant Hare Krishna generally don't need to sleep as much. For example, instead of sleeping eight hours, you could try sleeping six hours, thus giving yourself two additional hours in the day for chanting.
Srila Prabhupada told his followers that if we chanted a minimum of sixteen rounds daily and tried to avoid the offenses in chanting that by the end of our lives we would become pure enough to be eligible to return to the spiritual world. Any amount of chanting you're able to do regularly will bring you tremendous benefit, but the promise of eternal, blissful life without having to suffer future births and deaths in the material world is enough incentive for a lot of people to seriously consider aspiring to chant the minimum prescribed quota of sixteen rounds.