Having deflected questions so far regarding how much he knew about a federal project suspected of allowing guns sold in the U.S. to be illegally smuggled to Mexico, Attorney General Eric Holder is under fire again, this time from the National Rifle Association, a conservative group with a loud voice and influence in Washington.

Sources tell Fox News that NRA Executive Director Wayne LaPierre will call for Holder's resignation in a Saturday morning speech at the NRA's annual meeting in Pittsburgh.

LaPierre has criticized Holder's handling of "Project Gunrunner." The program of the Justice Department's Bureau of Alcohol Tobacco and Firearms is intended to stop the flow of guns to criminals in Mexico, but whistleblowers claim the bureau actually encouraged the illegal sale of firearms to known criminals, then allowed those guns to be smuggled to Mexico and tracked.

The practice of knowingly allowing guns to "walk" -- or be sold to straw buyers and then transferred to criminal organizations -- is against ATF policy. However, at least 15 ATF whistleblowers claim the agency, with the approval of Holder's Department of Justice, encouraged gun stores to make sales to questionable buyers, then failed to interdict the weapons.

According to Mexican authorities, at least 1,800 of those weapons were successfully smuggled into Mexico, where the cartels used them to commit crimes and foment violence.

What especially galls and upsets U.S. gun owners is this: While the ATF was allegedly sending guns south, hoping to eventually bust the entire trafficking organization, Obama administration officials, including President Obama and Secretary of State Hillary Clinton, were partly blaming U.S. gun stores for the violence in Mexico.

"This war is being waged with guns purchased not here but in the United States. ... More than 90 percent of the guns recovered in Mexico come from the United States, many from gun shops that lay in our shared border," President Obama said on a visit to Mexico on April 16, 2009.

That statement, which Holder expanded on a month later, laid the groundwork for the anger felt by U.S. gun owners. Many of them even accuse the administration of purposely fueling the violence in Mexico to justify tighter controls on the type of guns sold in the U.S. and where they can be sold.

"When does it stop being law enforcement and start being a criminal enterprise," La Pierre told CBS News. "Innocent people are dying. I mean artificially they set up straw man sales, to prove what? It is all under their watch."

Attorney General Holder has asked his department's inspector general to investigate the allegations.

But many say that isn't good enough, fearing the Justice Department will sweep serious allegations under the rug and allow guilty department officials to go unnamed.

Sen. Chuck Grassley, R-Iowa, and Rep. Darrell Issa, R-Calif., have each initiated congressional investigations that the ATF and DOJ have so far stonewalled. Issa has threatened to hold contempt hearings if subpoenaed documents are not handed over to his House Oversight Committee.

Holder is expected to appear before Congress this week on related issues.

In a statement Friday, the Department of Justice told CBS, "We have invited the NRA to join us and other stakeholders from across the spectrum in working to find common-sense solutions to keep guns out of the hands of people who are not legally allowed to possess them. They have yet to come to the table with any productive suggestions, but we hope they will reconsider."

LaPierre has said: "Why should I or the NRA go sit down with a group of people that have spent a lifetime trying to destroy the Second Amendment in the United States?"

The NRA consistently ranks as one of the most powerful lobbying organizations in Washington. It spent $10 million in the 2008 Presidential election.