javascript object max size limit

There is no such limit on the string length. To be certain, I just tested to create a string containing 60 megabyte.

The problem is likely that you are sending the data in a GET request, so it's sent in the URL. Different browsers have different limits for the URL, where IE has the lowest limist of about 2 kB. To be safe, you should never send more data than about a kilobyte in a GET request.

To send that much data, you have to send it in a POST request instead. The browser has no hard limit on the size of a post, but the server has a limit on how large a request can be. IIS for example has a default limit of 4 MB, but it's possible to adjust the limit if you would ever need to send more data than that.

Also, you shouldn't use += to concatenate long strings. For each iteration there is more and more data to move, so it gets slower and slower the more items you have. Put the strings in an array and concatenate all the items at once:

var items = $.map(keys, function(item, i) {
  var value = $("#value" + (i+1)).val().replace(/"/g, "\\\"");
  return
    '{"Key":' + '"' + Encoder.htmlEncode($(this).html()) + '"' + ",'+
    '" + '"Value"' + ':' + '"' + Encoder.htmlEncode(value) + '"}';
});
var jsonObj =
  '{"code":"' + code + '",'+
  '"defaultfile":"' + defaultfile + '",'+
  '"filename":"' + currentFile + '",'+
  '"lstResDef":[' + items.join(',') + ']}';

Step 1 is always to first determine where the problem lies. Your title and most of your question seem to suggest that you're running into quite a low length limit on the length of a string in JavaScript / on browsers, an improbably low limit. You're not. Consider:

var str;

document.getElementById('theButton').onclick = function() {
  var build, counter;

  if (!str) {
    str = "0123456789";
    build = [];
    for (counter = 0; counter < 900; ++counter) {
      build.push(str);
    }
    str = build.join("");
  }
  else {
    str += str;
  }
  display("str.length = " + str.length);
};

Live copy

Repeatedly clicking the relevant button keeps making the string longer. With Chrome, Firefox, Opera, Safari, and IE, I've had no trouble with strings more than a million characters long:

str.length = 9000
str.length = 18000
str.length = 36000
str.length = 72000
str.length = 144000
str.length = 288000
str.length = 576000
str.length = 1152000
str.length = 2304000
str.length = 4608000
str.length = 9216000
str.length = 18432000

...and I'm quite sure I could got a lot higher than that.

So it's nothing to do with a length limit in JavaScript. You haven't show your code for sending the data to the server, but most likely you're using GET which means you're running into the length limit of a GET request, because GET parameters are put in the query string. Details here.

You need to switch to using POST instead. In a POST request, the data is in the body of the request rather than in the URL, and can be very, very large indeed.