It's true that this can happen - it happened to me with my first baby - but as to when induction becomes necessary that is a grey area and as Schmickers said will mostly be determined by the policy of the careprovider.

Around 12-24 hours with no contractions seems to be the limit most places. Recently a mum I worked with had a hindwater leak at 2.30am and by 8am her OB was insisting on a drip (6hrs). I have known other women who have gone 24-72 hours just keeping an eye on their temperature (as a warning sign for infection).

The statistics on this say that about 80% of women will start labour within 24 hours of water breaking.

Most hospitals will insist that you go in when your water breaks, but as with anything it is entirely up to you whether or not you do so, once you weigh up your options. After you go in you're on the clock, so if nothing happens in 6-12 hours generally you're going to experience pressure to get labour going artificially.