The Obama administration's decision to try Osama bin Laden's son-in-law in federal court in New York City instead of a military tribunal at Guantanamo Bay has reignited a debate over how to deal with suspected terrorists.

It also recalls one of the largest failures of President Obama's presidency: His unfulfilled promise as a candidate in 2008 to close the detention center at Guantanamo Bay.

As Osama bin Laden's son-in-law, Sulaiman Abu Ghaith, pleaded not guilty to conspiring to kill Americans in New York Federal Court today, Republicans in Congress were criticizing the Obama administration for prosecuting a suspected al Qaeda terrorist in a civilian court just about a mile from the 9/11 memorial built over Ground Zero.

"Abu Ghaith has sworn to kill Americans and he likely possesses information that could prevent harm to America and its allies," Senate Minority Leader Mitch McConnell, R-Ky., wrote in a statement. "He is an enemy combatant and should be held in military custody."

Related: Osama Bin Laden's Son-In-Law Pleads 'Not Guilty'

The White House claimed there was a "broad consensus" across the federal government, from the Department of Defense, the Department of Justice and the Department of Homeland Security, to prosecute OBL's son-in-law in civilian court.

"The intelligence community agrees that the best way to protect our national security interests is to prosecute Abu Ghaith in an Article III court," Principal Deputy White House Press Secretary Josh Earnest told reporters today.

"We're able to question him as a part of the regular process in detaining individuals like this, but we're also able to put him through Article III courts to ensure that he's held accountable for his crimes," Earnest added. "This is somebody who's going to be held accountable for his crimes and … that will be done in accordance with the laws and values of this country, and it will be done so in a pretty efficient way."

Still, McConnell said that the administration's justification "makes little sense" and the intelligence community "deserve[s] the same access to intelligence and methods of defeating the enemy available to the team that found Bin Laden."

"At Guantanamo, [Abu Ghaith] could be held as a detainee and fulsomely and continuously interrogated without having to overcome the objections of his civilian lawyers," McConnell said.

Rep. Mike Rogers, R-Mich., the chairman of the House Permanent Select Committee on Intelligence, said civilian court "is not the appropriate venue" and the administration "should treat enemy combatants like the enemy."

"Al Qaeda leaders captured on the battlefield should not be brought to the United States to stand trial," Rogers said. "The president needs to send any captured al Qaeda members to Guantanamo."

A spokesman for House Speaker John Boehner, who opposes closing Guantanamo and previously fought against efforts by the Obama administration to prosecute 9/11 suspects in New York City, said the speaker "agrees" with Rogers.

New York Republican Rep. Pete King, R-N.Y., said he preferred that Abu Ghaith face trial in a military tribunal rather than civilian court, and he questioned what type of standard today's hearing could set.

"While a federal court trial of Abu Ghaith in lower Manhattan would not present the same security issues as a trial of Khalid Sheikh Mohammed, I strongly believe as a matter of policy that military tribunals are the proper venue for enemy combatants," said King, a member of the House committees on Intelligence and Homeland Security. "If the Abu Ghaith trial does go forward in federal court, it must not be used as a precedent for future enemy combatants who should be tried at Guantanamo."

But not all members of Congress oppose the administration's actions.

New York Democratic Rep. Jerrold Nadler, who represents the congressional district where Ground Zero is located in lower Manhattan, said he is "pleased Sulaiman Abu Ghaith will have to face justice in New York."

"I have long urged that we try terrorists in our civilian courts under the laws of the United States. We have done so successfully in the past, and we must continue to do so," Nadler, D-N.Y., said in a statement. "We are a nation committed to the rule of law, and we will demonstrate our values to the world even in the face of the most despicable mass murder in our history."