When setting a breakpoint in a member method javafx webkit causes an error. See http://snag.gy/nQMks.jpg for where it fails but also where it works fine. In jdk8 before 8u20 this does work.
I think the issue is this flag added in commit which appeared in the last 8u20 -
http://cr.openjdk.java.net/~msladecek/rt-36256/webrev/modules/graphics/src/main/java/com/sun/javafx/tk/quantum/QuantumToolkit.java.udiff.html
After adding the following *inPulse* flag, debugger API stop working when the breakpoint is set inside the function which is declared as a member of an object. I guess when the function is declared that way it also requires nested event loops, which is not handled in the patch.

Stack trace:
{code}
java.lang.IllegalStateException: Nested event loops are allowed only while handling system events
at com.sun.javafx.tk.quantum.QuantumToolkit.enterNestedEventLoop(QuantumToolkit.java:506)
at com.sun.javafx.webkit.EventLoopImpl.cycle(EventLoopImpl.java:59)
at com.sun.webkit.EventLoop.fwkCycle(EventLoop.java:45)
at com.sun.webkit.Timer.twkFireTimerEvent(Native Method)
at com.sun.webkit.Timer.fireTimerEvent(Timer.java:83)
at com.sun.webkit.Timer.notifyTick(Timer.java:64)
at javafx.scene.web.WebEngine$PulseTimer.lambda$static$44(WebEngine.java:1167)
at javafx.scene.web.WebEngine$PulseTimer$$Lambda$67/10449826.pulse(Unknown Source)
at com.sun.javafx.tk.Toolkit.lambda$runPulse$28(Toolkit.java:314)
at com.sun.javafx.tk.Toolkit$$Lambda$134/26908315.run(Unknown Source)
at java.security.AccessController.doPrivileged(Native Method)
at com.sun.javafx.tk.Toolkit.runPulse(Toolkit.java:313)
at com.sun.javafx.tk.Toolkit.firePulse(Toolkit.java:340)
at com.sun.javafx.tk.quantum.QuantumToolkit.pulse(QuantumToolkit.java:451)
at com.sun.javafx.tk.quantum.QuantumToolkit.pulse(QuantumToolkit.java:431)
at com.sun.javafx.tk.quantum.QuantumToolkit.lambda$runToolkit$363(QuantumToolkit.java:298)
at com.sun.javafx.tk.quantum.QuantumToolkit$$Lambda$40/33541029.run(Unknown Source)
at org.eclipse.swt.internal.win32.OS.DispatchMessageW(Native Method)
at org.eclipse.swt.internal.win32.OS.DispatchMessage(OS.java:2549)
at org.eclipse.swt.widgets.Display.readAndDispatch(Display.java:3759)
{code}