REPUBLICANS HAVE a potentially strong case to make against the Obama administration’s handling of Libya, as the latest political developments there underline. On Sunday, a disputed vote in parliament led to the swearing-in of a new prime minister — the sixth since former dictator Moammar Gaddafi was overthrown in 2011 with the help of U.S. and NATO air forces. The new leader, an Islamist from the city of Misurata, replaced pro-Western prime minister Ali Zeidan, who was driven out of the country this year after his government proved unable to stop a militia from filling a tanker with stolen oil.

From the safety of Europe, Mr. Zeidan conceded what was obvious all along: Libya’s post-Gaddafi government has no army and no way of establishing its authority over the hundreds of militias that sprang up in the vacuum that followed the revolution. Libya has fragmented into fiefdoms, its oil industry is virtually paralyzed, massive traffic in illegal weapons is supplying militants around the region and extremist groups such as Ansar al-Sharia, which participated in the Sept. 11, 2012, assault on the U.S. Consulate in Benghazi, are unchecked.

The Obama administration and its NATO allies bear responsibility for this mess because, having intervened to help rebels overthrow Gaddafi, they then swiftly exited without making a serious effort to help Libyans establish security and build a new political order. Congress might usefully probe why the administration allowed a country in which it initiated military operations to slide into chaos.

Instead, House Speaker John Boehner announced Friday that he would ask the House to create a select committee to investigate the Benghazi attack and the administration’s alleged attempt to cover up how and why Ambassador J. Christopher Stevens and three other Americans were killed. To the extent that it zeroes in on the behavior of White House aides and other U.S. officials in Washington following the Benghazi attack — as it appears likely to do — the investigation will address the least substantial and blameworthy aspect of the Libya record.

Numerous investigations and congressional hearings already have established the basic facts: U.S. intelligence agencies initially judged that the Benghazi attack was spontaneously inspired by reports of protests outside the U.S. Embassy in Cairo, and it “evolved into a direct assault” by heavily armed militants. That account was turned into talking points for then-Ambassador to the United Nations Susan Rice.

More than a year of efforts by GOP congressmen and conservative media to prove that Ms. Rice or the White House conspired to cover up the fact that Benghazi was a “terrorist attack” rather than a spontaneous act have gone nowhere, because there are no supporting facts. A recently released e-mail written by National Security Council aide Ben Rhodes reveals a not-so-scandalous proposal to argue that the Cairo and Benghazi protests did not prove “a broader failure of policy.” What’s missing is any evidence that Mr. Rhodes or anyone else knew the facts of Benghazi to be other than what was initially reported by U.S. intelligence. In fact, while an authoritative version of the Benghazi assault is still missing, the account cannot be ruled out.

Republicans may calculate that scandal-mongering about a Benghazi cover-up may rally the base before the fall’s elections. What it’s not likely to do is hold the Obama administration accountable for its actual failings in Libya.