HttpWebRequest With Kerberos Authentication?

I am trying to connect to a web service that uses Kerberos Authentication to authorize the user, but all I get is a 401 unauthorized everytime I try to make the request. Below is the code that I am using.

public XPathNavigator GSASearch(string url, string searchString)
{
HttpWebRequest request = (HttpWebRequest)WebRequest.Create(url + searchString);
request.CookieContainer = new CookieContainer();
request.Credentials = CredentialCache.DefaultCredentials;
request.ContentType = "text/xml";
request.Method = "POST";
HttpWebResponse response = (HttpWebResponse)request.GetResponse();
Stream receiveStream = response.GetResponseStream();
XPathDocument doc = new XPathDocument(receiveStream);
return doc.CreateNavigator();
}

EDIT: I feel I should explain a bit more what I am attempting to do. I have been tasked with providing a new interface for my company's Google Search Appliance. I am using an ASP.NET page, which does some things like choose a Collection depending on where a user is located, etc. and then sends the appropriate search string the the GSA. This was all working well until they decided to turn authentication on, and now I can't get any results (I either get a 401 unauthorized, or a message stating that 'Data at the root level is invalid'). If I take the search string and provide it directly to the GSA, it authenticates fine, and displays the results, I just can't seem to get it through the HttpWebRequest.

EDIT 2: I did a little more looking (ran the request through Fiddler) and it looks like the request is only attempting Negotiate and not Kerberos. I set the credentials to use Kerberos explicitly as below, but it didn't help...

public XPathNavigator GSASearch(string url, string searchString)
{
CredentialCache credCache = new CredentialCache();
credCache.Add(new Uri(url), "Kerberos", CredentialCache.DefaultNetworkCredentials);
HttpWebRequest request = (HttpWebRequest)WebRequest.Create(url + searchString);
request.CookieContainer = new CookieContainer();
request.PreAuthenticate = true;
request.Credentials = credCache;
request.ContentType = "text/xml";
request.Method = "POST";
HttpWebResponse response = (HttpWebResponse)request.GetResponse();
Stream receiveStream = response.GetResponseStream();
//StreamReader readStream = new StreamReader(receiveStream);
XPathDocument doc = new XPathDocument(receiveStream);
return doc.CreateNavigator();
}

EDIT 3: Ok, looking closer again, the CredentialCache.DefaultCredentials doesn't appear to have my network credentials in it...