You can do this using the WebRequest class.

WebRequest req = WebRequest.Create(tokenUri);
req.AuthenticationLevel = System.Net.Security.AuthenticationLevel.MutualAuthRequested;
req.Credentials = System.Net.CredentialCache.DefaultNetworkCredentials;
WebResponse resp = req.GetResponse();
StreamReader reader = new StreamReader(resp.GetResponseStream());
var token = reader.ReadToEnd().Trim();

This code reads the whole response into a variable called token.

To use NTLM see John's answer. If you need to have headers across sessions look at the CookieContainer property on the HttpWebRequest object. You will need to keep a reference to your CookieContainer and attach it to any other HttpWebRequests you make.