10. 93 - 7 would override any veto and the President knew it.
I'm not happy with the policies you refer to, but this obstructionist congress has repeatedly forced the President into a corner. Also, as any rational person would do, for the first year and a half of his term he tried to be "reasonable" and negotiate. Unfortunately everything he put forth was filibustered by McConnell. I'm sure if he had a filibuster-proof majority in congress he would not have supported NDAA. As it stands I'm sure he's waiting for the Supremes to overturn it. Or, even better, given the majority he needs in congress he will submit legislation to overturn it.