Buchanan last week was one of several members who said he is worried about the idea of a 12-member committee agreeing to spending cuts that the rest of Congress is expected to accept in an up-or-down vote.

"In the past, massive legislative measures have been written in the middle of the night by a handful of members and staff, and then quickly passed into law before the American people have a chance to even see what the final version looks like, let alone determine how they feel about it," he said. "This is not acceptable."

Sen. Dean HellerDean HellerNew CBO score triggers backlash Overnight Healthcare: CBO fallout | GOP senators distance themselves from House bill | Trump budget chief blasts score | Schumer says House bill belongs 'in the trash' Five takeaways from the CBO healthcare score MORE (R-Nev.) last week introduced a similar bill, S. 1501, that would require the supercommittee to work transparently.

Also last week, Sen. David VitterDavid VitterOvernight Energy: Trump set to propose sharp cuts to EPA, energy spending Former La. official tapped as lead offshore drilling regulator Former senator who crafted chemicals law to lobby for chemicals industry MORE (R-La.), Heller and four other Republican senators called on Senate leaders to ensure the supercommittee operates openly. Vitter has introduced S. 1498, which would require more reporting on contributions made to members of the supercommittee.

House Minority Leader Nancy Pelosi (D-Calif.) last week also called for an open process in the committee. "Without regard or respect for the recent S&P comment on our nation's credit rating, it is important to note the role that transparency and accountability play in making their judgment," she said.

Under the debt-ceiling agreement approved last week, House and Senate leaders must choose members of the new committee by Aug. 16.

-- This post was updated at 12:33 p.m.