Is there any way to retrieve a page\'s javascript variables from a Google Chrome Content Script?
If you know which variables you want to access, you can make a quick custom content-script to retrieve their values.
In popup.js :
chrome.tabs.executeScript(null, {code: 'var name = "property"'}, function() {
    chrome.tabs.executeScript(null, {file: "retrieveValue.js"}, function(ret) {
        for (var i = 0; i < ret.length; i++) {
            console.log(ret[i]); //prints out each returned element in the array
        }
    });
});
In retrieveValue.js :
function returnValues() {
    return document.getElementById("element")[name];
    //return any variables you need to retrieve
}
returnValues();
You can modify the code to return arrays or other objects.