Is it bad to add JSON on HTML data attribute?

Instead of storing everything in the data attribute you could use an identifier to access the data.

So for example you could do this :

var myBigJsonObj = { 
                      data1 : { //lots of data}, 
                      data2 : { //lots of data}                   

                   };

and then you had some html like so :

<div data-dataId="data1" id="x">

You can use jquery to get the data now like so :

var dataId = $('#x').attr('data-dataId');

var myData = myBigJsonObj[dataId];

This is the best approach imho.