I have made two attempts in trying to access a website with authentication, and I am not sure what is wrong with my attempts. I will list each one. Has anyone tried this and gotten it to work?
This should not be difficult for Java Android programmers to understand, nor should it matter that I am using monodroid EDIT (It DOES matter, because I have a Java implementation below that works just fine)END EDIT.
I am trying to gain access to an SSRS RDL through the WebView and I need to plug in some generic credentials.
ACTIVITY:
    public static string username = "...";
    public static string password = "...";
    public static string website  = "http://10.0.0.5/Reports";
    private WebView webView;
    private void setupWebView(int attempt)
    {
        webView.Settings.JavaScriptEnabled = true;
        webView.Settings.BlockNetworkLoads = false;
        switch (attempt)
        {
            case 1:
                {
                    webView.SetHttpAuthUsernamePassword(website, "", username, password);                                              
                }break;
            case 2:
                {
                    webView.SetWebViewClient(new AuthenticationClient(this));                        
                }break;
        }
        webView.LoadUrl(website);
    }
    protected override void OnCreate(Bundle bundle)
    {
        base.OnCreate(bundle);
        webView = new WebView(this);
        setupWebView(1);//1 or 2 depending on what I am testing
        // Set our view from the "main" layout resource
        SetContentView(webView);           
    }
}
AuthenticationClient:
    //DECLARED IN ANOTHER FILE
    [Android.Runtime.Register("android/webkit/WebViewClient", DoNotGenerateAcw = true)]
    public class AuthenticationClient:WebViewClient
    {
        private Context _context;
        public AuthenticationClient(Context context)
        {
            _context = context;
        }
        public override void OnReceivedError(WebView view, ClientError errorCode, string description, string failingUrl)
        {
            Toast.MakeText(_context, "OnReceivedError: " + errorCode, ToastLength.Long);
            //base.OnReceivedError(view, errorCode, description, failingUrl);
        }
        public override void OnPageStarted(WebView view, string url, Android.Graphics.Bitmap favicon)
        {
            Toast.MakeText(_context, "OnPageStarted: " + url, ToastLength.Long);
            //base.OnPageStarted(view, url, favicon);
        }
        public override bool ShouldOverrideUrlLoading(WebView view, string url)
        {
            Toast.MakeText(_context, "ShouldOverrideUrlLoading: " + url, ToastLength.Long);
            view.LoadUrl(url);
            return true;
        }
        public override void OnReceivedHttpAuthRequest(WebView view, HttpAuthHandler handler, string host, string realm)
        {
            Toast.MakeText(_context, "OnReceivedHttpAuthRequest: " + host, ToastLength.Long);
            handler.Proceed(Activity1.username, Activity1.password);
        }
    }
    //END DECLARATION
ATTEMPT 1: It does not even try to load the page. I keep getting an error: 
chromium(18710): external/chromium/net/http/http_auth_gssapi_posix.cc:463: [0821/095922:WARNING:http_auth_gssapi_posix.cc(463)] Unable to find a compatible GSSAPI library
ATTEMPT 2: Does not show a single toast message.
I have already looked at:
http://developer.android.com/reference/android/webkit/WebView.html
Using WebView setHttpAuthUsernamePassword?
WebView.setHttpAuthUsernamePassword() not working?
Passing username and password to SSRS 2005 reports from web application
OTHER STUFF 
I have now done it in Java and it works fine. I still need a Mono for Android solution:
public class Android_reporttestActivity extends Activity {
public static String username = "...";
public static String password = "...";
public static String website = "http://10.0.0.5/Reports";       
private WebView setupWebView()
{
    WebView webView = new WebView(this); 
    webView.setWebViewClient(
        new WebViewClient(){
            public void onReceivedHttpAuthRequest(WebView view, HttpAuthHandler handler, String host, String realm)
            {                           
                handler.proceed(username,password);
            }
        }
    );
    return webView;
}
@Override
public void onCreate(Bundle savedInstanceState) {
    super.onCreate(savedInstanceState);
    WebView webview = setupWebView();
    // Set our view from the "main" layout resource
    setContentView(webview);
    webview.loadUrl(website);
}