“Sadly, it seems that it will take holding the attorney general in contempt to communicate that evasiveness is unacceptable,” Mr. Matheson said in a statement. “It is a vote I will support.”

The vote will come as Congress tries to beat a Sunday deadline to reach deals on a major transportation bill and to extend subsidies for some student loans. On Tuesday, lawmakers gave final approval to bipartisan legislation overhauling user fees for the Food and Drug Administration.

But glimmers of cooperation are not likely to be seen in the acrimonious debate over the contempt vote. The political posturing and rhetoric leading to Thursday’s showdown mirror imbroglios past, especially the vote of a Democratic House in 2008 to hold Joshua B. Bolten, chief of staff in the Bush White House, and Harriet E. Miers, then White House counsel, in contempt over their refusal to turn over documents related to the firing of United States attorneys.

As in that case, the speaker of the House is talking about the need for the House to perform its oversight role against a stonewalling White House, and a minority leader is bristling over vital Congressional work being shunted aside for a partisan witch hunt.

The players have swapped roles, however. Speaker John A. Boehner, Republican of Ohio, was the minority leader then, and Representative Nancy Pelosi, Democrat of California, now the minority leader, was the speaker. But sub rosa conspiracy theories about gun control have turned the contempt vote into something more than a power struggle between government branches. Publicly, the House is deciding whether the attorney general has overstepped his authority by withholding documents about the Justice Department’s response once details about Fast and Furious were revealed. Privately, lawmakers must consider how the vote will be seen by the N.R.A., gun enthusiasts and hunters in their districts.

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“There is a belief among a lot of people — and I believe it, too — that Fast and Furious was a political attack on the Second Amendment and that the Justice Department facilitated a crime to further their gun control political agenda,” Mr. LaPierre said. “This whole executive privilege assertion is the last gasp of a cover-up.”

Gun Owners of America, a gun lobby considered more uncompromising than the N.R.A., released a letter to Representative Joe Donnelly, a Democrat running for the Senate in Indiana, demanding his contempt vote.

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“This is an issue of utmost importance to Second Amendment supporters in Indiana and throughout the country,” the group wrote.

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To White House officials, such assertions are bewildering. Fast and Furious was started by the Phoenix office of the Bureau of Alcohol, Tobacco, Firearms and Explosives to track guns as they moved into Mexico from United States gun dealerships. Seeking to build a bigger case against high-ranking gunrunners, agents did not move quickly against weapons obtained by low-level smugglers, and they lost track of 2,000 guns, most of which probably reached Mexican drug cartels.

Two were found near the scene of a shootout in which a United States Border Patrol agent, Brian Terry, was killed.

N.R.A. leaders are convinced that the operation was started to prove the Justice Department’s contention that 90 percent of the weapons fueling the Mexican drug wars come from the United States and that tighter gun laws are needed. Representative Darrell Issa, Republican of California, reflected that view on national television on Sunday.

“We have e-mail from people involved in this that are talking about using what they’re finding here to support the — basically assault weapons ban or greater reporting,” Mr. Issa, chairman of the House Oversight and Government Reform Committee, said on ABC’s “This Week.”

The committee has yet to produce those e-mails.

Among the thousands of pages of internal e-mails and documents Congressional investigators have gathered about the operation, they found a few showing that A.T.F. officials considered using some examples of documented gun flows to build a case for requiring greater reporting of multiple “long gun,” or rifle, sales by federally licensed gun shops. They singled out AK-47 assault-style rifles and their variants.

But the gun lobby is convinced that the documents being withheld would prove a far-reaching conspiracy to build support for a gun control agenda in a second Obama administration.

A vast majority of Democrats are not buying it.

“The idea that they spread a whole lot of guns around to foment gun crimes and then call for more gun control is a very peculiar line of reasoning,” said Representative Brad Miller, Democrat of North Carolina, who says he will vote no on the contempt measure.

But, he conceded, he is not running for re-election.