I think this is one of those "foreign policy actions" hchutch is granting to the Presidential power.
How much of the conduct of foreign policy is left to Congress and how much to the President?
It seems to me that the Constitution was designed to give the President a fair amount of leeway - particularly in cases when Congress is not in session. Congress has ways they can check the President's power - they can cut off funds (see the Boland Amendment), they can prohibit activities via legislation, and in extreme cases, they can use impeachment.
In terms of backing out of a treaty, especially one with an "out" clause like the ABM Treaty, it seems to me the President has the authority to do so. However, at the same time, Congress can introduce a resultion disapproving of the withdrawl or prohibit the expenditure of funds for any activity that would violate the terms of that treaty - and it would be subject to the normal process there (including a veto).
I do not see anything that indicates that there should be any less than ONE voice in foreign policy or military matters. Congress can CHECK the President on this, but at the same time, their efforts to set policy can be checked by a veto from the President.