Majority in Congress can override a veto? What kind of country do you want America to be? One that has no qualms about putting women in harm's way? Do we really think the people pushing for this sort of equality have actual people's best interest at heart?
"The White House has threatened to veto the defense bill due to other provisions that the administration’s Office of Management and Budget called “attempts to micromanage” the Department of Defense. However the overwhelming number of Senators who approved the bill would be more than enough to override a veto."
Senate approves women registering for the draft by CNN, June 15, 2016
"Override of a veto - The process by which each chamber of Congress votes on a bill vetoed by the President. To pass a bill over the president's objections requires a two-thirds vote in each Chamber. Historically, Congress has overridden fewer than ten percent of all presidential vetoes." senate.gov