Right now, lawmakers are in the final stages of negotiations on the must-pass National Defense Authorization Act, a bill that sets defense policy. One of the final sticking points is a provision called the Russell Amendment, which authorizes taxpayer-funded discrimination. The provision would require that all federal agencies allow religiously affiliated contractors and grantees to discriminate in employment on the basis of religion when using taxpayer money. This sweeping amendment extends well beyond the Defense Department and defense-related contracts and grants.
I will add that Obama's veto might not be possible because the National Defense Authorization Act is a must enact proposition.