First - they believe they have so re-defined the DoI, USC & BoR that they can use their deviant definitions as the hammer to reach their agenda. (They are not entirely wrong, here.) Even HuffPo endorses reading the USC & DoI annually - here.
Second - They understand that they simply have no possibility of reaching their goals without claiming the authority to do so exists within the USC & BoR. The documents are simply too entrenched in the American psyche to be ignored or dismissed. They can only be forced into contortions to fit the agenda. This is also their weakness. Whoever gets to have the final word on the meaning and intent of the DoI, USC and BoR will win the great masses.
Anyone trying to set a course for America toward Liberty with a touchstone other than the USC is pissing up a rope. Too many people, on both sides of the Liberty discussion, accept the USC as the North Star.
I dare say more people in America put faith into the USC than the bible. Before you dismiss that assertion - think about it. The overwhelming majority of people in America who are religious accept the USC as the foundation for governance (regardless of how they define the details). However, the overwhelming percentage of Liberals and other flavors of Reds in America pay only lip service to religion - if they even bother that much - but every Leftist politician claims the Constitution grants them the power and authority to do what they wish to do on the political field. I truly believe the guys holding the bible AND the Constitution will win - but the forces aligned who only hold the Constitution are formidable.
Third - More and more Bad People are calling for .Gov to prosecute "Domestic Terrorists". They want 'Hate Groups' prosecuted for 'Hate Speech'. They want gun owners prosecuted for owning guns. They want 'Mental Defectives' (anyone who wants a gun) to be shunned from society. Can we say Alien & Sedition Acts?
Connect the dots, folks. An awful lot of bible-carrying, Constitution-respecting 'Republicans' will support item 3 above.
Brace for impact. The crater will be epic.