WASHINGTON — The National Rifle Association has joined a Republican push to make Attorney General Eric H. Holder Jr. the first sitting cabinet member to be held in contempt of Congress, turning a once obscure fight over a gun-smuggling investigation into a proxy war over gun control.

Both the N.R.A. and the smaller but more strident Gun Owners of America have made Thursday’s House contempt vote crucial to their ratings of House lawmakers. The N.R.A. is pressing to win Democratic votes, said Wayne LaPierre, the group’s chief executive, and White House officials and House Democratic leaders concede that a handful of Democrats are likely to vote for the contempt resolution.

That may be more a testament to the enduring power of the gun lobby than to the bipartisan belief that Mr. Holder and the Obama administration have stonewalled Congress over the gun-smuggling investigation known as Operation Fast and Furious.

“Some members will consider the recommendations of the N.R.A.,” said Representative Steny H. Hoyer, Democrat of Maryland, the House minority whip.