Obama could bypass the senate using the sole-executive clause.

[link to en.wikipedia.org]
A sole-executive agreement can only be negotiated and entered into through the president's authority (1) in foreign policy, (2) as commander-in-chief of the armed forces, (3) from a prior act of Congress, or (4) from a prior treaty.[1] Agreements beyond these competencies must have the approval of Congress (for congressional-executive agreements) or the Senate (for treaties).

He could claim since it's arms that it's under foreign policy/commander in chief... so he doesn't need the senate...