"In 1999, when the US Senate considered giving its advice and consent to ratification, it declined to do so. In the hearings and floor debate, the verifiability of the treaty and the effectiveness of the US nuclear weapons stockpile in the absence of nuclear-explosive testing were principal issues cited as problematic. "
This article addresses these issues, and says that the Obama administration has declared its support for the Senate to ratify this treaty.
Four or five months ago the Obama administration got Iran to open up its nuclear facilities for international inspection along with other nuclear activities. These are described in the following article. This agreement ends July 20. To help continue these efforts to stop Iran from building a nuclear weapon the US should show the world its good faith along the lines of nuclear proliferation and sign the Comprehensive Test Ban Treaty. This would show the world that the US is committed in not testing any new weapons. The US hasn't tested any weapons in decades but signing this treaty would show the world we are committed to this policy. This is also the ethical and moral thing to do.
It would also put conservatives who have opposed this treaty into defending the position of supporting nuclear weapons testing. I think of Johnson's ad against Goldwater and the little girl pulling flower petals with a mushroom cloud in the background.