Q110. "Does the President have the authority to cancel the 1972 ABM treaty without the advise and consent of the senate? The power is given to the President to make treaties with the advise and consent of the Senate. I would think he does not have unilateral power to void a treaty."
A. There is some debate on the answer to this question, mostly because just about every conceivable route has been taken. The Constitution does not address the issue directly, so the question is, can we infer what the Constitution would say about breaking treaties? The first argument is in your question — that the President makes treaties, but the Senate must ratify them, so it must be that both the Senate and the President must agree to break the treaty. However, the President is head of state, and as such has responsibility for conducting foreign relations, and should have the ability alone. Lastly, since breaking a treaty can cause a major international incident, and even result in war, a final argument says that Congress as a whole must request the breaking of a treaty.
All of these methods have been used. Congress has unilaterally broken treaties, the President has unilaterally broken treaties, the Senate and the President have joined forces to break treaties, and the Congress has requested that the President break treaties — and in some cases, the President has refused. The safest way, meaning the way least likely to be challenged in court, is for the President and Congress to agree that a treaty needs to be broken and to do it together. Any other way invites controversy, though often times such controversy is unavoidable.
For a comprehensive look at how treaties have been broken over the centuries, refer to the Government Printing Office's page on The Executive, and look for "Termination of Treaties by Notice."