The House has voted, and Attorney General Eric Holder has been held in contempt for failing to hand over documents related to the disastrous gun-walking sting, Operation Fast and Furious. Problem is, at this point, there's almost nothing left for Congress to do.

The vote tally was largely along partisan lines: 255 yeas, 67 nays, with one present. Democrats walked out nearly en masse before the vote: 110 representatives did not vote. Today's vote is also different from last week's contempt citation by the House Committee on Oversight and Government Reform, which set the layup for today's full House vote. This one's the real deal. But even with Holder now officially held in contempt, he is not likely to be prosecuted, according to an analysis of likely outcomes by CNN. The reason is fairly simple: what Congress is asking the Justice Department to do is to prosecute itself.

It begins with allegations by Republicans (and some Democrats) that Holder knew – and approved – an alleged plan by the ATF's Phoenix Field Division to allow firearms to "walk" into Mexico, and into the hands of the cartels. The ATF pulled the plug after the shooting death of Border Patrol tactical officer Brian Terry by border bandits in December, 2010. An AK-47 variant rifle found at the scene was traced to Fast and Furious. Thousands of internal DoJ documents requested by congressional investigators were never turned over, though Holder was ordered to by a subpoena. But the documents may never be seen due to Obama administration's assertion of executive privilege hours before last week's citation.

But first, let's break down what the House voted to do, exactly. One, the House today authorized criminal charges to be filed against Holder. But the decision to file criminal charges is left up to Ronald Machen, the U.S. Attorney for the District of Columbia – who answers to Holder. (Machen is also an Obama administration appointee.) The chances of Machen filing charges against his boss? Around zilch. And even then, the administration has sent the documents down the memory hole, meaning Holder is immune from prosecution.

There's also a history (perhaps unsuspectingly) of not following through with prosecution when administration officials are held in contempt. In 2008, a Democratic Congress held White House Counsel Harriet Myers and Chief of Staff Josh Bolten in contempt for failing to turn over documents related to the dismissal of federal prosecutors. Neither Miers or Bolten were charged by the Bush administration's Justice Department. The last time an administration official was prosecuted for contempt, EPA official Rita Lavelle, was in 1983.

The other option, and more likely, is that House Republicans will move forward on civil charges. If House Republicans pursue this option, some documents may be turned over, but this would likely be long after public interest has waned. The civil case against Miers and Bolten was resolved in 2009, after Bush had gone into retirement, and the public – and political – notice given was minor. Obama's assertion of executive privilege also makes it slim investigators will get what they want, too.

"Just by going to court, the House guarantees it loses," Josh Chafetz, a law professor at Cornell University, told CNN. "Even if (the House) wins, it's going to be years from now. This Congress will be out of office and Obama may be out of office. If they wind up going to court, it will actually be to the great detriment of the House's oversight role."

And all of this will occur as the details of Fast and Furious are subject to greater scrutiny. Katerine Eban of Fortune reported Wednesday that instead of intentionally allowing guns to walk, the ATF's Phoenix office was instead paralyzed by incompetence, internal conflicts and weak gun laws that allowed smugglers to move freely. Though, in at least one case, an ATF agent reportedly used taxpayer money to buy pistols for a weapons trafficker.

Such disclosures could be one of Holder's primary defenses if a civil suit goes forward. If failures over gun-walking was isolated to Phoenix, then Holder is insulated. But if documents reveal that Holder knew about the plan (or perhaps e-mails by Holder in the early days of the scandal's disclosure), then he – or at the least, his job – could be in trouble.

That is, emphasis on *could *be in trouble. Now, that doesn't mean we won't see any documents arising out of a civil suit. But don't hold your breath, and don't expect any charges.