President Bush will unilaterally obligate the United States. Neither the Senate (pursuant to its constitutional role in ratifying treaties) nor the House will have any say. While the reduction of the Senate and House to ciphers in national security matters through executive agreements flouts the Constitution, it has become as commonplace as the rising and setting of the sun. It is no longer news.
If the Senate does not reassert itself, its treaty power will disappear like the Cheshire cat. Even major arms control agreements will become unilateral executive exercises. An empire will have replaced a republic.