This claim is dumb. With a nod to John Aravosis (I couldn't find the link, but I know it was his), I might just as well claim, "I could turn seventy in sixteen days, if only I were sixty-nine years and 349 days old today."
The Washington Post reports that the National Intelligence Estimate gives a shortest timeframe of ten years.
Personally, I am very uncomfortable taking this at face value and saying "the Iranians are at least ten years away". The estimate depends on both technical factors, and assumptions about Iranian policy choices, and it is very difficult for us to judge how heavily it leans on each of them. If most of the hurdles are due to lack of resources in the Iranian project or due to IAEA constraints, then there may be room for considerable acceleration by policy choices to devote more resources, or withdraw from NPT. As Richard Wilson has maintained, the Osirak attack led to Iraqi policy choices which likely accelerated the Iraqi nuclear program of the 1980's. If on the other hand the timeline is primarily constrained by technical issues, ten years may be very difficult to shorten by policy choices. As the full NIE on Iranian development is not available, Americans cannot judge how vulnerable the ten year estimate is to different assumptions about Iranian policy choices.
In fact, I find it very difficult to imagine a technical reason it must take ten years. There are no obvious reasons, though perhaps there are non-obvious ones. For instance, there's a report about moly in Iranian ore, that I'd love to hear more about.
Cat Dynamics also has a number of speculations on how the plutonium timescale could be shortened. I believe that the Russian enriched uranium fuel was not delivered. But I'd love to have someone clear that point up definitively.
That said--whether the time is ten years, or somewhat shorter or longer, the timescale is certainly measured in years. Sixteen days is dumb.