Why isnt my HttpClient timing out?

Question

I have some code like the following:

using (var client = new HttpClient())
{
  client.Timeout = TimeSpan.FromMilliseconds(3000);
  var request = new HttpRequestMessage(HttpMethod.Head, myURI);
  var response = await client.SendAsync(request);
}

But when I go into the debugger, the code just hangs on await client.SendAsync(...). It throws no exception, and the control does not continue. It hangs indefinitely. Does anyone know what I am doirn wrong?