Meteor ticks the boxes for a realtime web application; "one language", "realtime as default". It looks like it eases the path of development, automatically updating your front end templates when your data changes by implementing an subscription model.
Web forms really tries. You define your HTML in an aspx file - these are basically your templates. Elements can be set to have a data source which will, for example, infill the data for the element from your database. Elements can also be set to post back to the server anytime they change, get clicked or what have you.
Postbacks are tied to events in the C# code behind pages which means that you can move all your logic server side. It makes developing for the web more like writing a traditional style windows client application.
Of course it isn't without it's downside. The ViewState - a massive chunk of data that kept....state between page loads. That's a nasty piece of work. Ingenious in it's own way, but nasty when you bump up against it. And of course there is the enormous expense of re-rendering the entire page every time a select box that is wired up to post back to the server changes. Large Web forms applications can become sloooooow on the client side.
Meteor does something similar. Only now with baked in Ajax goodness, the applications actually feel useable. I wonder if Microsoft missed the boat? I wonder if they could have leveraged Web forms, or something like it, to be more like Meteor. Maybe they do now - Web forms is still alive and well, but I haven't (thank goodness) had to use it in a very long time so I'm somewhat out of touch.
Where Microsoft really shine, in my opinion, is with their IDE. Wiring up server side events to a button click really is easy - just open up your aspx file (the template), double click on the button and Visual Studio will wire up the event for you and pop you into the server side event so you can write your code. On a large page, this really does take some pain away. You don't make stupid typos wiring up your button because you don't have to type it in. It know Vim is awesome and all, but this part of the developer experience, Microsoft really does well.
Somewhere in the future, I imagine the best of both worlds. Something like Meteor + Visual Studio all open sourced and ready to go.