chrome.tabs.onUpdated.addListener(function(tabId, changeInfo, tab){
function(tabId, changeInfo, tab){
    //using tab.url and XMLHttpRequest() i get newText for:
    chrome.browserAction.setBadgeText({text: newText});
   };
});

chrome.tabs.onUpdated.addListener(function(tabId, changeInfo, tab){
    function(tabId, changeInfo, tab){
        if(!changeInfo.url) return; // URL did not change
        // Might be better to analyze the URL to exclude things like anchor changes

        /* ... */
        chrome.browserAction.setBadgeText({text: newText}, tab.id);
    };
});

chrome.browserAction.setBadgeText({text: newText}, tab.id);  //<<this is not working to me

 chrome.browserAction.setBadgeText({text: "Phish", tabId: tab.id}); //<<This is working to me