By default, within popup.js/popup.html, the document object refers to the extension's popup window's document only. To get the DOM for a specific tab (for instance the currently active tab), you would need to use content scripts communications. For example we need to send a request from the extension to your content script via popup, so in the popup.html you do something like this:

chrome.tabs.getSelected(null, function(tab) {

  // Send a request to the content script.

  chrome.tabs.sendRequest(tab.id, {action: getDOM}, function(response) {

    console.log(response.dom);

  });

});

Now in the content script, we need to listen for those events coming from the extension, so in some file we named dom.js

chrome.extension.onRequest.addListener(function(request, sender, sendResponse) {

 if (request.action == getDOM)

   sendResponse({dom: The dom that you want to get});

 else

   sendResponse({}); // Send nothing..

});

Now remember to setup your manifest to include the content script and tab permission.