– President Obama’s top national security aides on Sunday defended the deal that freed an Army sergeant captured in Afghanistan in exchange for five senior Taliban officials held at the detention center at Guantanamo Bay, Cuba, as the Taliban’s leader hailed the release as “a great victory.”

Defense Secretary Chuck Hagel said Sgt. Bowe Bergdahl’s health was deteriorating and that his life was in danger, while White House National Security Adviser Susan Rice said the deal met “a sacred obligation” to bring Bergdahl home.

Prominent Republican lawmakers continued their criticism of the deal, however, as Bergdahl, who spent nearly five years in Taliban custody, arrived at a U.S. military hospital in Germany for medical treatment and debriefing by intelligence experts. It was uncertain when he would return to the United States.

At a news conference in Boise, Idaho, Bergdahl’s parents, Jani and Bob Bergdahl, who met with Obama on Saturday at the White House, said they had yet to speak with their son, which Bob Bergdahl said was by design. “If he comes up too fast, it could kill him,” Bob Bergdahl said, comparing his son to a deep-sea diver who must go through slow decompression when surfacing.

In a rare statement, Taliban leader Mullah Omar credited “the sacrifice of our mujahedin” for leading to the release of “our senior leaders from the hands of the enemy” and called for the release of “all those who have been imprisoned for defending the honor and freedom of their country.”

In comments on Sunday morning news programs, Republicans were unanimous in saying the deal would embolden U.S. enemies to take other U.S. hostages and that Obama had violated a law that requires that Congress be notified 30 days in advance of any release of Guantanamo detainees.

Obama advisers fired back by saying Republicans would be in full attack mode if the U.S. government had squandered an opportunity to gain Bergdahl’s release.

Speaking to reporters traveling with him in Asia, Hagel also left open the possibility that the circumstances of Bergdahl’s capture might one day be investigated, but said that was not the Pentagon’s first priority. Bergdahl was first noticed missing from his base in Afghanistan on June 30, 2009. There were allegations that he left the base voluntarily.

Sen. Ted Cruz, R-Texas, said the United States had paid “a very dangerous price” for Bergdahl’s freedom.

Suggesting that the United States could have used military force to rescue Bergdahl, Cruz said: “The reason why the U.S. has had the policy of not negotiating with terrorists is because once you start doing it, every other terrorist has an incentive to capture more soldiers.”

Hagel dismissed that line of criticism. “As we know certainly from what we’re dealing with all over the world today with terrorist groups, they take hostages,” Hagel said. “They take innocent schoolgirls. They take businesspeople. They will take any target that they can get to. So, again, our focus was on the return of Sgt. Bergdahl.”

New details also emerged about the exchange, a logistically complicated swap that required coordination across 8,000 miles and years of hatred and distrust.

The deal called for the Taliban to move first, a U.S. official involved in the release effort said, surrendering Bergdahl to U.S. forces in eastern Afghanistan. Once that had been accomplished, the five Taliban were to be brought from their cellblocks at Guantanamo and turned over to Qatari diplomats, who other officials said had arrived at the detention center on Friday. The detainees and their Qatari escorts then boarded a U.S. aircraft for the flight to Qatar.

Rice, also on “This Week,” said the government of Qatar had a “detailed understanding” with the United States over the security of the five released detainees, who are to remain in Qatar for at least a year.

Rice acknowledged that Obama had skirted the law by not notifying Congress of plans to release the detainees. But she said lawmakers should not have been surprised by what developed because lawmakers “were well aware that this idea and this prospect” were in the works because of “extensive consultations with Congress” about earlier talks to free Bergdahl.

That explanation didn’t satisfy Sen. John McCain, who was a prisoner of war in Vietnam.

McCain said he was disturbed that the Taliban had chosen the detainees to be released from Guantanamo. He branded them “the hardest of the hard-core.”

All five were on the Obama administration’s indefinite detention list, a status that meant they were slated to be held forever by the United States, without facing criminal charges. Their transfer dropped the number of such “forever prisoners” held at Guantanamo from 43 to 38.