"to put your neck on the line" ("on" not "out") means to take a big risk (often bravely) and expose yourself to potentially bad consequences. The idiom may come from what happens to chicken in factories when they are being slaughtered. Here is an example: "If you criticise your boss publicly for his bad behaviour, you will really put your neck on the line."

There is another expression, "to stick your neck out" which means that you may be taking a risk when you say something. http://idioms.thefreedictionary.com/stick+neck+out So your phrase sounds like a mixture of two...

I think it is a mix of two Idioms 'Put your neck on the block' - make yourself vulnerable, like a chicken, ready for to be turned into food. "Are you willing to put your neck on the block to get this proposal through?" (you will be in big trouble if your proposal fails) 'Stick your neck out' the same as above, but also means 'to expose yourself to risk, in order to help another. "you really stuck your neck out for me then (I thought my proposal was going to fail, but you spoke up to support me, when it was risky to do so)