What did Obama mean by " ... something like this might have happened again"?
Solution 1:
Here is my interpretation:
The pronoun this in the sentence actually refers to another shooting took place in 2009 at the same facility that resulted in 13 deaths by Maj. Nidal Malik Hasan, a military psychiatrist and a Muslim. It was an act of terrorism. One of his motivations was to kill as many soldiers as he could to wage jihad on American military personnel.
The verb might in the sentence expresses the possibility that the Fort Hood incident is similar to the one took place in 2009. But so far nobody is sure if the Fort Hood incident is actually terrorism-related.
The commander, Lt. Gen. Mark A. Milley, told reporters that the soldier's motive remained unclear, but that the shooting did not appear to be related to terrorism.
(It is highly likely that it had nothing to do with terrorism at all as there are strong evidence that Ivan A. Lopez had a medical history that indicates an unstable psychiatric or psychological condition.)
Solution 2:
Rather than
We’re heartbroken something like this might have happened again.”
I think he wants to say
We’re heartbroken something like this has happened again.”
but needs to say
We’re heartbroken something like what this might be might have happened again.”
but can't say the first as it would be stating on the record that "this" is in fact "something like what this might be", and can't say the second because it's just too wishy-washy. So he gets caught between the desire to be emotional and direct, and the caution required of a government official discussing possibly criminal events.