JSON and Postgres Variable Queries

I’m having an issue with JSON requests in Postgres and was wondering if anyone had an answer.

I have an orders table with a field called “json_data”.

In the json data there is a plan’s array with an id value in them.
{ "plan”: { “id”: “1” } } }

I can do regular queries that will work, like so:
SELECT json_data->>’plan'->>’id' as plan_id FROM orders;

But if I try to query on the data that is returned it will fail:
SELECT json_data->>’plan'->>’id' as plan_id FROM orders WHERE plan_id = 1;
OR
SELECT json_data->>’plan'->>’id' as plan_id FROM orders GROUP BY plan_id;
OR
SELECT json_data->>’plan'->>’id' as plan_id FROM orders ORDER BY plan_id;

Is this something that has been overlooked? or is there another way to go about this?

I’ve tried everything from the documentation here:
http://www.postgresql.org/docs/9.3/static/functions-json.html

I’ve attached a json dump of the orders table.

Thanks in advance,

Joey