Ted at Point of Law pointed out that Senator Coburn has introduced the companion bill to H.R. 1359. This bill is called the Enumerated Powers act, and is supposed "To require Congress to specify the source of authority under the United States Constitution for the enactment of laws, and for other purposes."

This week, Sen. Coburn, along with 22 other Republican co-sponsors, including Sen. John McCain, introduced the corresponding S. 3159. Still no Democrats on board this basic good-government principle.

Source: PointofLaw.com | PointOfLaw Forum: Enumerated Powers Act on Senate-side

I have no problem with the idea of the bill.  Congress should always make sure that it isn't exceeding its authority when enacting law.  But this bill is a waste of time.  Why?  In order to comply with the act, the act itself states its source of authority:

(a) Constitutional Authority for This Act- This Act is enacted pursuant to the power granted Congress under article I, section 8, clause 18, of the United States Constitution and the power granted to each House of Congress under article I, section 5, clause 2, of the United States Constitution.

Source: THOMAS (Library of Congress)

Article I, Section 8, Clause 18 of the Constitution is referred to by political science professors and high school teachers everywhere as "the elastic clause" because it can expand to cover just about anything Congress wants to do.  While the intent of this bill is to ensure Congress carefully considers whether it has authority to enact a law, the real effect of it will be to cause this Article I, Section 8, Clause 18 boilerplate to be inserted into probably 75 out of 100 bills, with the Commerce Clause boilerplate going into another 20.    In principle, this bill is a good idea.  In practice, it's just a vehicle to allow a group of conservatives the opportunity to showboat for groups like the Federalist Society.