A number of Republican House freshmen who came to Washington promising to slash government spending are increasingly worried that the congressional supercommittee, to which that task has now fallen, is operating too much in secret and that the lack of transparency could doom the enterprise.

Despite a few open sessions, including one on Tuesday, they worry that the panel’s mostly private negotiations will produce a result that does not represent the kind of revolutionary change they had hoped to bring to the Capitol.

Some are concerned that the legal mandate of the 12-member panel — to cut the deficit by $1.2 trillion to $1.5 trillion over the next decade — is too small. Some fear that they may be asked to sign on to the group’s product in December, without much time to review it, and warned of dire consequences if they do not get on board.

But most of all, they are disappointed that the supercommittee has been operating almost entirely behind closed doors. Though the group held its fifth public hearing Tuesday, its members have spent hours huddled behind closed doors and have offered only vague public comments about the progress of their talks.

“I don’t think anyone would view this as a completely transparent process,” said Rep. Bill Huizenga (R-Mich.), who had wavered over whether to support the August deal that created the panel but ultimately came on board. “Some argue you can’t have that. I think we need to have that.”

The lack of transparency has caused grumbling throughout Congress, with members lamenting that their supercommittee colleagues have been as tight-lipped with fellow lawmakers as they have been with reporters. But it has been especially upsetting for freshmen who ran last year railing against Washington’s backroom deals.

“I understand how it’s difficult to get things done in a body this size. But at the same time, the secrecy is really scary,” said Rep. Randy Hultgren (R-Ill.). “I understand the difficulty they’ve got and the pressure they’re under. But I’d rather err on the side of more information and more input, rather than an easier process.”

The committee was established in the August deal to raise the debt ceiling and is designed to help break through the gridlock that often prevents Congress from tackling big issues. Its members must agree to a deficit-reduction strategy by Nov. 23.

The House and Senate must then conduct an up-or-down vote on the proposal — no amendments or Senate filibusters allowed — by Christmas.

And there are stiff consequences for failure. If the supercommittee cannot come up with a deal, or if its recommendations are rejected by the rest of Congress, the federal budget will be automatically cut by $1.2 trillion over the next decade, split between security and domestic programs.

The across-the-board hit is designed to be painful enough to compel an agreement.

But the hesi­ta­tion of some freshmen suggests that the supercommittee’s recommendations may face the type of challenge that has become familiar in the House since Republicans took over in January. A bloc of Republicans might reject the supercommittee’s strategy, despite the fact that the group was formed specifically to tackle the problem that propelled many of them to office.

And while their opposition may not prove fatal, it means that Republicans will probably have to rely on the votes of House Democrats to get the recommendations approved.

That helps explain some of the pressure that has fallen on the 12 supercommittee members, who must devise a plan that is acceptable to their opponents but not seen as a capitulation or betrayal by their allies.

By all reports, the supercommittee remains at an impasse. Republicans last week rejected a Democratic proposal to reduce the deficit by $3 trillion in part by raising $1.3 trillion in new tax revenue. Democrats then rejected a Republican offer to cut more than $2 trillion without raising taxes by cutting entitlements more deeply.

Even after word of those proposals leaked, supercommittee members declined to fully detail the offers or comment about them publicly.

Criticism has been particularly fierce among the 29 House freshmen who opposed the August debt deal that created the supercommittee.

“I have yet to find a single person in my district who approves of 535 members of Congress delegating this serious responsibility to a mere 12 members,” said Rep. Mo Brooks (R-Ala.), who complained that supercommittee members have told their colleagues that they are operating under a “cone of silence.”

“The people in my district are appalled, frustrated and angry by the process,” Brooks said.

Rep. Joe Walsh (R-Ill.), elected a year ago with tea party backing, called the supercommittee “a stupid idea” that appears no better for its weeks of quiet work than it did back in August. “We came to Washington to make the hard decisions to turn this country around,” he said. “Putting that on some other committee instead of us doing our job? Shame on us.”

Some of those who backed its creation said the special committee might not have been their first choice for approaching deficit reduction but was a necessary concession to the Senate during August’s bruising fight over the debt ceiling.

And some urged patience.

“We have a model put into place,” said Rep. Mike Kelly (R-Pa.), who had exhorted fellow Republicans to rally around their leaders at a GOP meeting not long before the August deal was approved. “Let’s let it play out. . . . Sometimes we weigh in too early, and we start throwing stones.”

But even among those who backed the supercommittee’s creation, a number said they saw its recommendations only as a first step, and promised to push for deeper reforms and a balanced-budget amendment to the Constitution to force deeper cuts in the future.

“I’ve told our members, ‘I love you guys, and I’ve got great confidence in you,’ ” Huizenga said. “But I’ve got little confidence in the ability of the structure to work.”