The House Oversight Committee has voted to hold Attorney General Eric Holder in contempt for not tuning over documents related to the Fast and Furious operation. The vote was down party lines, with 23 Republicans voting in favor and 17 Democrats voting against. President Obama allowed Holder to invoke executive privilege Wednesday.

Update: So what's next? The contempt citation will now be considered by the full House of Representatives, NBC News' Pete Williams explains. Republican leaders have seemed uncomfortable with the committee's actions so far. "You have a situation where you have Eric Cantor and John Boehner both resisting this call to have a contempt citation, so you have a division within the Republican ranks that diminishes profoundly the clout of the committee," Geraldo Rivera said on Fox News this month. "The committee looks more and more radical to their own Republican leadership." Politico, too, reported that Republican leaders think the Fast and Furious fight is getting the party off message. And yet, after Obama asserted executive privilege Wednesday, Boehner seemed to embrace the controversy, with his spokesman calling Obama's decision evidence of a "cover up."

If the House votes in favor of the contempt citation, Williams explains, it gets sent to the U.S. district attorney in Washington, D.C., but "from there on, it gets complicated." Williams says:

The Justice Department has long taken the position, as a separation of powers matter, that Congress cannot force the Justice Department to undertake a prosecution of an executive branch official. The courts have never resolved the question. 

The Justice Department, under both Democratic and Republican administrations, has further claimed that a U.S. attorney must not initiate a prosecution when the president has asserted executive privilege over what Congress seeks.