Washington (CNN) -- A letter sent to President Barack Obama will outline why his invocation of executive privilege over documents sought by lawmakers investigating the botched Fast and Furious gun-running sting is either "overbroad, or simply wrong," House Oversight Committee chairman Darrell Issa said Sunday.
The letter will be sent later Sunday or Monday, Issa, R-California, told ABC's "This Week." The oversight committee voted Wednesday to refer a potential contempt citation against Attorney General Eric Holder to the full House, which is set to vote this week.
"We're past that part of the discovery, relative to contempt, Issa said. "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.
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."
Obama's assertion of executive privilege over some of the documents sought by the panel means the Justice Department can withhold specified materials.
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 Hlder because he is fighting their efforts to suppress voter turnout in November.
Holder said on 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.
Boehner, R-Ohio, has said the executive privilege assertion proved White House involvement and indicated a cover-up, which Carney rejected.
CNN's Tom Cohen contributed to this report.