WebGL would be extremely tricky for them -- they'd first have to port their OpenGL render pipeline to JavaScript, which would be "doable I guess" especially since they could just port their GL ES (mobile) render paths, that's mostly identical to WebGL. But they'd also have to port their entire runtime library to JS, which would exceed a major rewrite in terms of effort I believe. And then they're calling .NET / Mono APIs everywhere in their own runtime/core code, I'm sure. And then there's the thousands of Unity projects out there calling said APIs. And then, and then, and then...
Next, asset loading but since you're on the web, ideally you'd have smarter on-demand streaming of compressed assets, rather than a 10-minute-long "Loading Game Assets" splash-screen page...
I remember seeing an interview with the Unity CEO and he said that they had someone who was looking into (evaluating) HTML5 as a Unity target platform. I guess that would include WebGL, but also things like the Web Audio API and WebSockets.
My impression is that the web browsers aren't quite there yet, in terms of support for all the necessary functionality required by a modern 3D video game. For example, IE doesn't support WebGL.
Take this with a grain of salt, but I vaguely remember some moment when everyone was talking about the announced ability to export to Flash, and a question mentioning HTML 5 or WebGL came up: their (unofficial?) response was something along the lines that they would do whatever it takes to be on any platform they need to if there is demand. I feel they have proven that they really care about wide multi-platform availability, with efforts like their "Union" program and availability on console and mobile platforms. This recent move to support Linux shows that also. If WebGL proves itself to have a large critical mass of developers asking for it, I bet they will very very seriously try to do something. I can't speak to the difficulty of such a move, or compare the actual results of their Flash exporting efforts, but I don't doubt they would do it if it was reasonably possible and there was demand.
