chrome extension `sendResponse` does not work

You haven't stated weather you this code is in the content script or the background page. From looking at it I assume it it part of the content script.

I tried your code in one of my own extensions and it alerted "[object Object]" which is what happens when you alert a variable that isn't a string or numerical value. If you change the alert data to "response.responseData" it will alert the value you labeled "responseData" from the background page.

As it wasn't alerting anything for you I think that the script that is listening for the message is not responding properly.

I got the code working. This is the content script:

//Document ready
window.onload = function() {
    alert('Ready');
    //Send a message
    sendMessage();
}

//Get message from background page
chrome.runtime.onMessage.addListener(function(request, sender, sendResponse) {
    //Alert the message
    alert("The message from the background page: " + request.greeting);//You have to choose which part of the response you want to display ie. request.greeting
    //Construct & send a response
    sendResponse({
        response: "Message received"
    });
});

//Send message to background page
function sendMessage() {
    //Construct & send message
    chrome.runtime.sendMessage({
        method: "postList",
        post_list: "ThePostList"
    }, function(response) {
        //Alert the message
        alert("The response from the background page: " + response.response);//You have to choose which part of the response you want to display ie. response.response
    });
}

This is the background script:

//Get message from content script
chrome.runtime.onMessage.addListener(
    function(request, sender, sendResponse) {
        //Alert the message
        alert('The message from the content script: ' + request.method);//You have to choose which part of the response you want to display ie. request.method
        //Construct & send a response
        sendResponse({
            response: "Message received"
        });
    }
);

//Send message to content script
function sendDetails(sendData) {
    //Select tab
    chrome.tabs.query({active: true, currentWindow: true}, function(tabs) {
        //Construct & send message
        chrome.tabs.sendMessage(tabs[0].id, {
            greeting: sendData
        }, function(response) {
            //On response alert the response
            alert("The response from the content script: " + response.response);//You have to choose which part of the response you want to display ie. response.response
        });
    });
}

Every time a script receives a message you have to use the "sendResponse" function to send a response.

Hope this helped.

This same question Chrome Extension Message passing: response not sent will help.

You just need to add return true on listener.

I was looking for the solution to get data from content script inside the popup. Yes, you can have it with storage, but this is applied to all tabs, so better to send message to active tab, and read response:

inside popup.js

chrome.tabs.query({
    active: true,
    lastFocusedWindow: true
}, function (tabs) {
    chrome.tabs.sendMessage(tabs[0].id, {data: 1}, function (response) {
        console.log(response.data)
    });
});

inside content.js

chrome.runtime.onMessage.addListener(function (message, sender, sendResponse) {
    if (message.data === 1) {
        // accepts only 1 field
        sendResponse({
            data: 2
        });
        // very important to return true 
        return true; 
    }
});