This story has been updated.

The bipartisan debt-reduction supercommittee is holding its first private meeting Thursday — and not everyone is pleased about it.

Sen. Dean Heller (R-Nev.) said in a statement Wednesday that he is ‘disappointed’ that the 12-member panel will be meeting behind closed doors. The group plans to hold a private breakfast meeting Thursday morning, according to a Democratic aide who was not authorized to speak publicly about the panel’s schedule.

“The American people, along with my colleagues from both sides of the aisle, have repeatedly asked the Super Committee to ensure the integrity of its process by opening all of its meetings to the public,” Heller said. “I’m disappointed that they’ve decided to yet again ignore the American people’s right to know and have instead resigned to more inside-baseball negotiations. It is my fear that this first closed-door meeting will be the first of many. Given the extraordinary jurisdiction of this Committee, meetings should be held in full daylight for the public to see.”

Heller, a former House member who in May was sworn in as the successor to former Sen. John Ensign (R-Nev.), is one of seven Senate Republicans who have introduced a measure calling for members “to conduct the business of the Committee in a manner that is open to the public.”

The group has held two public gatherings so far — an organizational meeting last Thursday before President Obama’s jobs address to a joint session of Congress, and a public hearing yesterday examining the drivers of the country’s debt.

The joint committee, which was established under last month’s debt-ceiling legislation, has a Thanksgiving deadline by which to agree to a plan to achieve $1.5 trillion in deficit savings over the next decade or else $1.2 trillion in across-the-board cuts will be enacted. But the panel’s actual timeline became even shorter than that on Tuesday, when Congressional Budget Office Director Doug Elmendorf said that his office would need to receive a plan from the group by the end of October in order to have the proposal scored before the Thanksgiving deadline.

The transparency issue is one that members of both parties have brought up — House Minority Leader Nancy Pelosi (D-Calif.) has also called for the panel to conduct its work in as open a process as possible, and some outside groups such as the Sunlight Foundation have suggested that such closed meetings may in fact be a violation of the panel’s rules.

At last week’s initial meeting, the transparency issue did arise: Sen. Patty Murray (D-Wash.), co-chairman of the panel, entered into a discussion on the matter with Rep. Jeb Hensarling (R-Texas), the group’s other co-chairman. They said their understanding was that informal meetings were not subject to the same requirements as the group’s formal sessions.

“The House and Senate rules provide similar transparency requirements to those meetings as we have proposed in the rules of the Joint Select Committee,” Murray said. “And I just want to clarify that the use of the term ‘meeting’ in these rules has the same traditional meaning used in both houses and does not include less formal caucuses or working sessions that would not be covered by either the House or Senate rules in the normal or ordinary course.”

Hensarling replied that Murray was correct. “That reflects our understanding as we have been working on this particular rules package,” he said.

And as previous negotiations over the debt ceiling and avoiding a federal shutdown have shown, most deals that get made on Capitol Hill are hammered out behind closed doors — and as Sen. John Kerry (D-Mass.) suggested Tuesday, that may be particularly true for the debt supercommittee, which faces an ever-increasing task and an ever-decreasing timeframe within which to accomplish it.