You could log all the request and responses using onResourceRequested and onResourceReceived api's. I do this for a scraper I wrote in casperjs which uses phantomjs underneath. The Watir-Webdriver should provide some hook into webPage object of phantomjs.
page.onResourceRequested = function(requestData, networkRequest) {
console.log('Request (#' + requestData.id + '): ' + JSON.stringify(requestData));
};
page.onResourceReceived = function(response) {
console.log('Response (#' + response.id + ', stage "' + response.stage + '"): ' + JSON.stringify(response));
};