— Reporting by CBS News' Margaret Brennan, Kathryn Watson, Alan He, Eleanor Watson and Olivia Gazis

Hawks in the Republican Party are fuming over President Trump's abrupt decision to pull some U.S. troops from Syria, a move they say he made without consulting him. And the White House and Pentagon are offering sparse details on how such a withdrawal will work, with the White House and the Pentagon referring questions to each other Wednesday in the wake of the announcement.

"It's a catastrophic disaster," one senior administration official told CBS News "Face the Nation" host Margaret Brennan of the fallout from the president's decision, saying the national security team is working to mitigate that fallout.

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Meanwhile, some Trump allies on Capitol Hill including Sen. Lindsey Graham are blasting the president's decision, with Graham calling it an "Obama-like mistake" — something sure to irk the president.

It's unclear exactly how the president reached the decision to withdraw troops immediately from the war-torn country, and a different senior administration official who held a conference call with reporters Wednesday afternoon refused to discuss the process for arriving at that decision. As recently as the last few weeks, top administration officials have expressed the importance of having a presence in the region and that ISIS is still a threat there.

"It was the president's decision to make and he made it," the senior administration official, whose identity the White House did not wish to disclose, told reporters on the conference call.

The administration official did not deny that a contingent of ISIS remains in Syria, despite the president's tweet that ISIS is "defeated" in Syria, and the sole purpose of keeping troops there was for that reason. The official could not say how many troops have been sent home, if any, and referred questions about what the next phase is in the administration's strategy in the region to the Pentagon.

The National Counterterrorism Center's guidance from October suggests that while efforts to contain ISIS have seen substantial successes this year, the terror network remains "an adaptive and dangerous adversary," and in Iraq and Syria, its leaders are relocating to rural safe havens to "support a long-term insurgency." While the ISIS' safe havens in Iraq and Syria have "largely collapsed," it still maintains a robust global enterprise of nearly two dozen branches, each with "hundreds to thousands of members."

The president's decision prompted intense reactions particularly from Republican senators with foreign policy expertise. Graham, an unabashed supporter of the president, said he wants hearings immediately on how the decision was reached. Graham said his trip to Syria earlier this year made it "abundantly clear the approximately 2,000 American troops stationed there are vital to our national security interests." He said that an withdrawal of U.S. forces would also be a boon to America's rivals in the region, including Iran and Russia, as well as the terror group ISIS. Mr. Trump tweeted Wednesday that ISIS had been defeated. But in fact, ISIS still controls pockets of territory in the region.

Mona Yacoubian, the senior adviser for Syria, Middle East and North Africa at the United States Institute of Peace, said the U.S. military presence in Syria was a "small footprint but an important one," noting that U.S. troops are in Northeastern Syria where the Kurdish Syrian Democratic Forces have control of oil fields, gas, water and infrastructure. The U.S. has helped the SDF maintain control. And without the U.S., there will be a vacuum where ISIS, Iran and Russia could gain a foothold. There are still about 30,000 ISIS fighters in Syria, Yacoubian said.

Graham also highlighted the plight of Kurdish people in the area who have been allies in the fight against ISIS. "An American withdrawal will put the Kurds and all those who came to America's aid in destroying ISIS at tremendous risk," he said. "It will make it more difficult to recruit future partners willing to confront radical Islam. It will also be seen by Iran and other bad actors as a sign of American weakness in the efforts to contain Iranian expansion."

Florida Republican Sen. Marco Rubio made a similar argument to reporters on Wednesday, criticizing the troop withdrawal as a "colossal" mistake and "grave error" that would embolden Russia and China. "We will lose influence in the region, and I believe we will lose influence beyond the region as a result of this decision," he said.

Illinois Republican Rep. Adam Kinzinger, a sometime critic of the president, likewise criticized the move in harsh terms."History will look at that as one of the stupidest strategic moves before a negotiation," he told The Washington Post. "In order to have a successful diplomatic outcome, you have to have a military option and a military presence."

Kinzinger appeared on CNN with Jake Tapper later in the day, saying he's "speechless to "see the president wake up today and say we've defeated 'em, we know that's not true. Nobody would argue we've defeated them. That's not only going to hamper our operation, it's going to double or triple the ranks of ISIS."

Outgoing Sen. Bob Corker, the Republican chairman of the Senate Foreign Relations committee, said the president had "caught everybody off guard" with the decision.

"I doubt there is anybody in the Republican caucus in the Senate that just isn't stunned by this precipitous decision. It's just like he woke up in the morning and made it."