While building C# client binding to be loaded into a Unity 3D client, I checked the version of .NET Framework that Unity supports currently, and it turned out to be just up to .NET 3.5 (its really "mono" that is the gating factor, not Unity)
Too bad I can't use SignalR. Even version 1.0 of it requires .NET Framework 4.0 (and 2.0 required 4.5)
I should have checked this earlier so that I would have not built client's access layer using not just SignalR binding but also nice REST-friendly HttpClient - now I am re-doing that part using the good old WebClient.
The take away: if you are building a C# library to provide stubs for RESTful API, set the project's target .NET Framework version to "3.5 client".
As for WebSocket bindin, looks like https://websocket4net.codeplex.com/ is a good alternative, so I will try that.