Hobbes' answer to How long can a 2 person crew survive on ISS totally cut from Earth? has links to articles that include NASA press releases from around that time.
In Progress Failure Puts Burden on Upcoming Resupply Missions (after the M-27M failure), Jeff Foust wrote
In a presentation to a NASA Advisory Council panel here April 8, NASA officials said food supplies on the ISS would reach a threshold called “reserve level” on July 24, and go to zero on Sept. 5. That assumed that the station received no more supplies beyond a SpaceX Dragon cargo mission launched to the station in April [CRS-6 - Erin].
The other major limiting consumable is a solid waste container known by the Russian acronym KTO. Without additional cargo missions beyond the Dragon flight, KTO supplies would reach the reserve level July 20 and be exhausted on Sept. 2. Other consumables, including water, would not reach reserve levels until later in the year or early 2016.
After Progress M-28M arrived, Jeff Foust wrote in "Progress Arrives At Space Station, Easing Supply Concerns" for Spacenews that those estimates had been revised:
Michael Suffredini, NASA ISS program manager, said at a June 28 briefing that the station still had enough basic supplies, including food and water, to support its crew through October. The supplies on this Progress, he said, would extend that date by about a month.
The Spacenews article about the HTV-5 launch indicated that
The arrival of the HTV will further ease concerns about the station’s supply of food and other consumables that were under strain by a series of cargo mission failures in the last year. The additional cargo on board the HTV will extend station’s supplies through at least the end of the year.
In articles about Progress M-29M and Cygnus OA-4 I don't see any further estimates, indicating that the concern about continued supply flights had died down by that point.
However, treating the supply problems as a starvation concern is hyperbolic. This was always a loss-of-mission concern rather than loss-of-crew; if supplies had not arrived in time, the astronauts would have left the station in the Soyuz available to them and returned to Earth.
