House Republicans are threatening to shut down part of the State Department if the Obama administration doesn’t cough up more documents related to Hillary Clinton Hillary Diane Rodham ClintonJeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Momentum growing among Republicans for Supreme Court vote before Election Day Warning signs flash for Lindsey Graham in South Carolina MORE’s helming of the agency during the Benghazi attacks.

Frustrated Republicans believe using the power of the purse could force the administration to hand over documents related to the 2012 assault on a U.S. compound in Libya that killed Ambassador Christopher Stevens and three other Americans.

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“There’s a discussion. We haven’t come to a conclusion yet,” said Rep. Kay Granger Norvell (Kay) Kay GrangerBottom line Helping our seniors before it's too late House approves .3 trillion spending package for 2021 MORE (R-Texas), chairwoman of the House Appropriations subcommittee that oversees funding for State and foreign aid.

Funding could be withheld from the agency’s programs and efforts “unless it relates to our own national security or our allies,” she added.

In interviews with The Hill, Granger didn’t go into detail about what exactly could lose funding, but other GOP sources said divisions such as Legislative Affairs and Public Affairs and the Office of the Secretary could be affected at the department. Critical areas, including embassy security, would not be targeted.

Granger made the comments the same day Clinton called on her former agency to release emails she had turned over from her private server “as soon as possible.”

“Nobody has a bigger interest in getting them released than I do,” she said.

House Select Committee on Benghazi Chairman Trey Gowdy Harold (Trey) Watson GowdySunday shows preview: Election integrity dominates as Nov. 3 nears Tim Scott invokes Breonna Taylor, George Floyd in Trump convention speech Sunday shows preview: Republicans gear up for national convention, USPS debate continues in Washington MORE (R-S.C.) first floated the idea of using State Department funding as leverage earlier this month. In an interim report, he mentioned that the House should “consider motivating the executive branch through the appropriations process.”

The concept started picking up speed this week, with House Majority Leader Kevin McCarthy (R-Calif.) conceding “there is a chance of that happening.”

Senior Republicans, including other heads of Appropriations panels, say they’d also be on board.

Rep. Bill Flores William (Bill) Hose FloresPatient Protection Pledge offers price transparency Texas GOP lawmaker calls for 'carbon neutral' but 'energy dominant' future OVERNIGHT ENERGY: Biden calls climate change one of America's four major crises | National parks chief says coronavirus staff shortages shouldn't prevent access | Trump hits California officials over wildfires MORE (R-Texas), chairman of the conservative Republican Study Committee, said his party should “use every tool that’s at our disposal” to get the emails, while Rep. Mario Díaz-Balart (R-Fla.), a senior appropriator, called the appropriations process “the way we can get answers” from the administration.

“I’m open to anything. ... Trey Gowdy’s been more than a patient man, so something’s gotta change,” added House Oversight and Government Reform Committee Chairman Jason Chaffetz Jason ChaffetzThe myth of the conservative bestseller Elijah Cummings, Democratic chairman and powerful Trump critic, dies at 68 House Oversight panel demands DeVos turn over personal email records MORE (R-Utah), whose panel conducted its own Benghazi investigation in the last Congress.

Administration officials “have not been cooperative or transparent,” he said.

It wouldn’t be the first time Republicans threatened to slash funding to force the administration to cooperate. Last week, the GOP passed a defense policy bill that cuts nearly $500 million from the Pentagon’s budget unless officials turn over documents related to the prisoner swap of Taliban fighters for Army Sgt. Bowe Bergdahl.

“The American people have a right to know what happened in Benghazi, and we need to make sure that this doesn’t happen again to imperil future ambassadors,” said Rep. Vicky Hartzler (R-Mo.), the chairwoman of the Armed Services Oversight and Investigations Subcommittee.

Top Democrats dismissed the GOP’s Benghazi funding ploy as an empty threat and suggested the State appropriations bill never would become law because President Obama has threatened to veto any spending bills that implement “the current Republican budget framework.”

“Don’t they have anything better to do that’s more constructive?” asked New York Rep. Nita Lowey, who is both the top Democrat on the full Appropriations Committee and Granger’s subpanel.

“I think they should focus on the agenda and all the work we have to do,” she added, saying the Benghazi investigation is a “charade that’s wasting taxpayer money.”

Rep. Elijah Cummings (Md.), the top Democrat on the Benghazi Committee, also criticized the potential move.

“Reducing State Department funding and personnel will only further slowdown and drag out the Republican’s taxpayer-funded political attack on Secretary Clinton,” he said in a statement.

On Tuesday, the State Department disclosed that it wouldn’t release thousands of pages of emails from Clinton until Jan. 15, 2016.

That release date would come weeks before voters head to the polls in the early-voting states of Iowa and New Hampshire, potentially complicating Clinton’s White House bid.

Clinton responded by pushing for the department to release the emails sooner, and a U.S. federal judge rejected the agency's plan. It called for the messages to be released on a rolling basis.

Any delay could become a major hurdle for Clinton. Gowdy is insisting that the former secretary of State should appear before his panel 30 days after it has determined it has received all the documents it requested from the State Department.

GOP members of the Benghazi Committee have pounced on the issue of Clinton’s use of a personal email server while at Foggy Bottom to cast the nation’s former top diplomat as lacking transparency.

“We’re very interested in every email,” said Illinois Rep. Peter Roskam, one of seven Republicans on the Benghazi panel.

Another, Rep. Jim Jordan (R-Ohio), said that “in a general sense, the more information you have ... that helps you get to the truth when it’s time to go have a hearing and ask questions.”

“I’m open to anything that helps us get to the truth. Obviously, the power that the legislative branch has is the power of the purse, and so we’ll see,” Jordan added.

— Cristina Marcos contributed.