Washington (CNN) -- The U.S. House is expected to vote this week for the first time in history to cite a sitting U.S. attorney general for contempt of Congress, a GOP leadership aide told CNN on Monday.
The vote is scheduled for Thursday, said the source, who was not authorized to speak on the record.
The House Oversight Committee recommended the vote against Attorney General Eric Holder last week after he refused to hand over all of the requested documents in its investigation of the Bureau of Alcohol, Tobacco and Firearms' controversial Fast and Furious gun-running sting.
The vote came after President Barack Obama asserted executive privilege over some documents sought by the panel. The White House move means the Department of Justice can withhold some of the documents.
House Oversight Committee chairman Rep. Darrell Issa said Sunday that Obama's invocation of executive privilege is either "over broad, or simply wrong."
"We're past that part of the discovery, relative to contempt," Issa, R-California, told ABC's "This Week." "We know that there's a lot of wrong things and we want to fix it. What we're talking about now, when we get lied to, when the American people get lied to, there can't be oversight when there's lying."
"The Supreme Court held pretty clearly there cannot be executive privilege over a criminal cover-up," he said. "Lying to Congress is a crime. We have every right to see documents to say, 'Did you know?' 'What did you know?' including even the president."
However, he added, "If we get documents that do show, cast some doubt, or allow us to understand this, we'll at least delay contempt and continue the process. We only broke off negotiations when we got a flat refusal when we asked to get information needed for our investigation."
If the documents say what Holder claims they say, "we might dismiss contempt," he said.
Issa said last week he was surprised by Obama's action and questioned whether the White House's role in Fast and Furious "has been greater than previously acknowledged."
Sen. Charles Grassley of Iowa, the ranking Republican member of the Senate Judiciary Committee, told CNN he previously traced the program only up to the level of an assistant attorney general.
"Now it raises the question of what does the president know and when did he know it by the claim of executive privilege," said Grassley, who participated in last week's meeting.
Meanwhile, Rep. Elijah Cummings, D-Maryland and the ranking member of the oversight committee, called on House Speaker John Boehner to meet with Holder to resolve the dispute.
"I'm calling on Speaker Boehner to come forth and show the strong leadership that I know he will, and sit down with the attorney general to resolve this matter," Cummings said on "Fox News Sunday." "The attorney general has made it clear that he is willing to work with this Congress."
White House spokesman Jay Carney has called the Republican investigation a "politically-motivated, taxpayer-funded, election-year fishing expedition."
And House Democratic leader Nancy Pelosi, D-California, has said Republicans are targeting Holder because he is fighting their efforts to suppress voter turnout in November.
Holder said Thursday his offer to turn over some of the documents sought by House Republicans still stands.
But Issa told "Fox News Sunday" that absent the documents, the full House will vote Holder in contempt. A number of Democrats have appealed to the administration to be forthcoming, he said, and "many of them will stay with us."
Last week's events heightened the drama of the high-profile showdown between Issa and Holder over the Fast and Furious program, which dates back to subpoenas issued by the House committee last year.
The Bureau of Alcohol, Tobacco, Firearms and Explosives launched Operation Fast and Furious out of Arizona to track weapon purchases by Mexican drug cartels. However, it lost track of more than 1,000 firearms that the agency had allowed straw buyers to carry across the border, and two of the lost weapons turned up at the scene of the 2010 killing of U.S. Border Patrol agent Brian Terry.
Issa's committee is seeking documents that show why the Justice Department decided to withdraw as inaccurate a February 2011 letter sent to Congress that said top officials had only recently learned about Fast and Furious. However, Holder has refused to turn over materials containing internal deliberations, and asked Obama to assert executive privilege over such documents last week.
Like Grassley, Boehner, R-Ohio, has said the executive privilege assertion proved White House involvement and indicated a cover-up, which Carney rejected.
Issa and other Republicans on the panel have mentioned Terry's death by name in accusing Holder and the Justice Department of trying to stonewall the investigation of what happened.
"The Department of Justice has fought this investigation every step of the way," Issa said last week.
"At the heart of the congressional investigation into Operation Fast and Furious are disastrous consequences: a murdered Border Patrol Agent, his grieving family seeking answers, countless deaths in Mexico, and the souring effect on our relationship with Mexico," Issa said in a statement. "Congress has not just a right but an obligation to do all that it can to uncover exactly what happened and ensure that it never occurs again. "
Terry's family issued a statement Wednesday that called for all of the documents sought by the committee to be turned over.
"Our son lost his life protecting this nation, and it is very disappointing that we are now faced with an administration that seems more concerned with protecting themselves rather than revealing the truth behind Operation Fast and Furious," the statement said.
The mother of another federal agent said Wednesday she wants to know the "full truth" about his death.
Immigration and Customs Enforcement Agent Jaime Zapata, who was working for the United States in Mexico, was murdered in February 2011 when his vehicle was ambushed on a highway between Mexico City and Monterrey.
Sen. John Cornyn, R-Texas, last year said he wanted to know if a Texas-based "gun walking" program may have played a role in Zapata's murder. He said one of the weapons used in the slaying was allegedly purchased in Texas and trafficked to Mexico.
CNN's Kate Bolduan and Tom Cohen contributed to this report.