You have the JSON formatted incorrectly. It should represent 1 object with "cols" and "rows" properties. "cols" is an array of objects with "type" (string, mandatory), "label" (string, optional), "id" (string, optional), and "p" (object, optional) parameters. Rows is an array of objects with "c" (array, mandatory), and "p" (object, optional) parameters. The "c" parameter of a row object is an array of objects with "v" (string/number, mandatory), "f" (string, optional), and "p" (object, optional) parameters.
Your columns construction is correct, but you only need it once. Your rows construction needs some work. Let's start with this row:
["1","2013-08-13
00:00:00"]
should be:
{"c":[{"v":"1"},{"v":"2013-08-13
00:00:00"}]}
and this row:
["2","2013-08-13
00:00:00"]
should be:
{"c":[{"v":"2"},{"v":"2013-08-13
00:00:00"}]}
Add them to your "rows" array like this:
"rows":[{"c":[{"v":"1"},{"v":"2013-08-13
00:00:00"}]},{"c":[{"v":"2"},{"v":"2013-08-13
00:00:00"}]}]
You can then combine the whole thing together to make the JSON string:
{"cols":[{"label":"id","type":"string"},{"label":"date","type":"string"}],"rows":[{"c":[{"v":"1"},{"v":"2013-08-13
00:00:00"}]},{"c":[{"v":"2"},{"v":"2013-08-13
00:00:00"}]}]}