Use the default dispatcher where possible for nested message loops.

ui/views/widget/desktop_aura/desktop_dispatcher_client.cc

Index: ui/views/widget/desktop_aura/desktop_dispatcher_client.cc
diff --git a/ui/views/widget/desktop_aura/desktop_dispatcher_client.cc b/ui/views/widget/desktop_aura/desktop_dispatcher_client.cc
index be251da5c35cf77329f01eca9ebff2fd1f3bb1dd..977d0de222607d4209dcec736c0e0f27a2ef830d 100644
--- a/ui/views/widget/desktop_aura/desktop_dispatcher_client.cc
+++ b/ui/views/widget/desktop_aura/desktop_dispatcher_client.cc
@@ -4,6 +4,7 @@
 
 #include "ui/views/widget/desktop_aura/desktop_dispatcher_client.h"
 
+#include "base/auto_reset.h"
 #include "base/run_loop.h"
 
 namespace views {
@@ -23,7 +24,14 @@ void DesktopDispatcherClient::RunWithDispatcher(
   base::MessageLoopForUI::ScopedNestableTaskAllower allow_nested(loop);
 
   base::RunLoop run_loop(nested_dispatcher);
+  base::AutoReset<base::Closure> reset_closure(&quit_closure_,
+                                               run_loop.QuitClosure());
   run_loop.Run();
 }
 
+void DesktopDispatcherClient::QuitNestedMessageLoop() {
+  CHECK(!quit_closure_.is_null());
+  quit_closure_.Run();
+}
+
 }  // namespace views