I think this might be a case of confusion and cross-reporting.
US Exercise code-names are specific to particular commands, and it appears that "Austere Challenge" is a a USEUCOM exercise, not USCENTCOM. Indeed, the US Joint Forces Command summary of exercises for FY2011/2012 includes "Austere Challenge" as a USEUCOM exercise behind held in Germany in May 2012. The link Robrob provides confirms this is a European Command exercise, usually held in Germany.
If we go back to the
original article suddenly it all becomes clear.
Lt.-Gen. Mark Hertling, commander of the US Army in Europe, told The Jerusalem Post that the two armies will hold a massive ground forces exercise in Spring 2012 called “Austere Challenge,” which will seek to increase inter-operability between the IDF and the US Army.
The drill, which is unprecedented in its size, will include the establishment of US command posts in Israel and IDF command posts at EUCOM headquarters in Germany – with the ultimate goal of establishing joint task forces for the event of a future large-scale conflict in the Middle East.
According to the Joint Forces Command document:
AC is a USEUCOM-sponsored Command Post Exercise/Combined Arms Exercise in full spectrum operations with a major combat operations emphasis.
What we can safely garner for all of this is that the IDF are going to partake in the exercise in Germany by establishing a CPX, while an element of the US exercise will be complimentary US CPX in Israel.
This refutes the idea that there will be thousands of US troops in Israel; the FX part of the exercise will be in Germany, using EUCOM forces.
So what are all these troops? The article tells us what's really going on:
Shortly before Austere Challenge, scheduled for May, the EUCOM will also hold the Juniper Cobra missile defense exercise with the IDF, and include the Arrow 2 and Iron Dome as well as America’s THAAD (Terminal High Altitude Area Defense) and the shipbased Aegis Ballistic Missile Defense System. The exercise is expected to include the actual launching of interceptors from these systems.
Of course, "US missile defense troops conducting exercise with IDF" is hardly as exciting as "thousands of US troops deploying to Israel for biggest ever exercise" but hey, reality is seldom as exciting as fantasy.
ETA
Joint Forces document (PDF)
ETA2
It appears "Juniper Cobra" is a relatively small exercise (although the biggest field exercise the USA and Israel conduct in Israel) of hundreds of US ground troops, not thousands, and it has been held every second year since 2001, so nothing to see here...