I do not know of any built in way to do this. The scripting languages does not support Measures in that manner.
That only leaves arcobjects as your only possibility for accomplishing that task. However I strongly recommend not going in that direction. ("Just because you can does not mean you should!")
You would have to write code that would constantly have to read your current display cursor, determine whether it intersects a route, if it does, determine the intersection of the point the cursor is at with your line and then retrieve the "M" value and then display it as a tooltip. This would be running in the background all the time even when your are doing other stuff (May greatly slow down everything.)
-- my 2 cents
Thanks Ted, That's just the insight I was looking for. The effect would look exactly like what is shown via an edit session -> "Define Line Portion", I just wish it could be achieved outside of the edit session perhaps as another toolbar button as a quick way to explore measure values along the route. Thanks for your input/reply, Chris