The Hill says only 15 Republicans and no Democrats on the 40-member House Oversight and Government Reform Committee have publicly expressed support for Issa's resolution to hold Holder in contempt for not turning over documents related to the Operation Fast and Furious
The measure needs 21 votes to pass.
Two of the committee's 23 Republicans have said they aren't supporting the measure, and six other Republicans did not respond to The Hill's repeated requests for comments in the past two weeks, the Capitol Hill newspaper said Tuesday.
Issa has been investigating the "gun-walking" tactics of Fast and Furious for more than a year.
In Fast and Furious, Bureau of Alcohol, Tobacco, Firearms and Explosives agents allowed weapons to be illegally bought and circulated on both sides of the U.S.-Mexico border. Two of the weapons turned up after a U.S. Border Patrol agent was killed in southern Arizona a year ago, and many others reportedly were used in crimes in Mexico.
Last week, Issa criticized Holder on Fox News for not complying with a subpoena demanding Fast and Furious documents and said all Republicans on his committee backed the resolution.
"Members of my committee on the Republican side, to a person, are totally convinced," Issa said. "Our case right now, we're trying to work with the Democrats on the committee."