Sharp isn't Apple's only supplier. It is also getting screens from Japan Display and LG Display, Osawa reports. Apple should still be able to manufacture the new iPhone, it's just a matter of whether or not it will be able to make enough if one of its suppliers is behind schedule.
Reiji Murai at Reutersconfirms Osawa's report, but adds this wrinkle: "The Japanese display maker is struggling with high costs that have cut into its margins on the screens, raising the question of whether Apple might provide financial incentives to speed up production."
For what it's worth, Osawa says Sharp had delays when it was making the screen for the new iPad that launched earlier this year. There were no shortages of new iPads.