Like the military spending bill, it incorporates the newly negotiated agreement on banning torture of terror detainees and lays out the legal rights of those held in Guantánamo Bay, Cuba.
And on Wednesday he plans to deliver a third in the East Room of the White House, where he will propose new legislation on bringing terror detainees to trial.
Civil liberties lawyers welcome the US Supreme Court ruling on terror detainees.
Secretary of State Condoleezza Rice, in Europe this week, has been trying to answer charges that America routinely practices so-called extraordinary rendition, sending terror detainees abroad to places where they face possible torture.
Construction crews went to work Thursday morning as usual at Camp Six, putting final touches on a hulking, $24 million concrete structure that is to be the permanent, medium-security facility for terror detainees.
Most of the initial conservative attacks focused on her criticism of Bush administration's use of so-called torture against suspected terror detainees.
Following his tenure, he has been very critical of the Obama administration, especially its treatment of terror detainees, which was something that Cheney had great authority and experience over throughout his tenure.
These memos were accompanied by the Justice Department's release of four Bush-era legal opinions covering (in graphic and extensive detail) the interrogation of 14 high-value terror detainees using harsh techniques beyond waterboarding.
Indeed, just two months after the attacks of Sept 11, 2001, she had threatened to resign as national security adviser after Mr Bush authorised military commissions for terror detainees without informing her.
The debate is also driven in part by concern expressed by the Supreme Court about the exclusion of defendants when it struck down the Bush administration's original effort to put terror detainees on trial before military commissions.