Mike Pence comes out against the tax deal, and adds this caveat:

Pence also implied that the compromise is unconstitutional, saying, "this deal was largely negotiated by leaders in the Senate and the White House, despite the fact that the Constitution clearly says that bills relating to taxes should begin in the House of Representatives."  

The phrase "Constitutional conservative" has been popping up quite a bit the last few years, and figuring out what it means has been a little difficult. I think the true answer is that a Constitutional conservative is a conservative who believes any policy he disagrees with is unconstitutional.