The WebKit maintainers already refused adding Dart support on grounds of not being a web standard, not wanting to fragment the web any further and not wanting the extra maintenance burden for the changes required to WebKit in order to support multiple scripting languages. Same reasoning goes for Mozilla, especially because they don't see Dart solving any problems that either couldn't be solved in a future version of JavaScript or that warrant the pains of having to maintain two different scripting engines. AFAIK Opera also didn't show any interest in it.
So Google's only hope left is for Chrome to gain monopoly-level market share to simply force the remaining browsers into compliance.
So Google's only hope left is for Chrome to gain monopoly-level market share to simply force the remaining browsers into compliance.