"These special operators will over time be able to conduct raids, free hostages, gather intelligence and capture ISIL leaders," Carter said of the troops deploying to Iraq, adding that the U.S. is "at war."
But lawmakers at Tuesday's hearing expressed concern over the fact that the administration is taking these steps in the absence of an updated authorization for the use of military force (AUMF).
"You heard the secretary of defense today say both in writing and verbally that we are at war," Rep. Randy Forbes, R-Virginia, said to Gen. Joseph Dunford, Chairman of the Joint Chiefs of Staff, who also testified at the hearing.
"Who declared that war?" Forbes asked.
In the tense exchange, Dunford conceded that the administration did not have the authority to declare war.
"We are technically not at war ... Yet declared war," Dunford said.
The War Powers Resolution of 1973 requires that the president seek authorization from Congress within 60 days if sending U.S. troops into a conflict. And even those who support the anti-ISIS mission are starting to challenge the administration's assertion that military action against ISIS is covered under two previous AUMFs that were passed 14 and 15 years ago respectively.
"Now that you're telling us that we're sending special operations forces into Syria, can you tell me where in any one of those AUMFs there's the authorization to do that?" asked Rep. Bradley Byrne, R-Alabama, of Carter.
Byrne, who supports giving the administration additional war authority, isn't the only member to raise the issue in recent weeks.
Last month, a bipartisan coalition of 35 representatives penned a letter to new House Speaker Paul Ryan, in which they called for a vote on an updated AUMF.
"We do not share the same policy prescriptions for U.S. military engagement in the region," the members wrote. "But we do share the belief that it is past time for the Congress to fulfill its obligations under the Constitution and vote on an AUMF that clearly delineates the authority and limits, if any, on U.S. military engagement in Iraq, Syria and the surrounding region."
The U.S. began its air campaign against ISIS in August 2014, citing the two most recent AUMFs. The first is a 2001 authorization, passed in the days after the 9/11 attacks, which formed the basis for war in Afghanistan, but has also been used by both President George W. Bush and President Barack Obama to pursue terror targets around the world. The second is the 2002 authorization permitting the war in Iraq.
While Obama has previously called for the eventual repeal of both authorizations and for the passage of an ISIS-specific one, he maintains that the 2001 and 2002 AUMF provide the necessary legal cover for operations now taking place in Iraq and Syria.
In February, six months after the air campaign began, the Obama administration sent a new draft AUMF to Congress, but the measure didn't get far.
Republicans, by and large, argued for broader authorization that would allow Obama to target ISIS with few limitations. Democrats meanwhile, called for stronger limitations to avoid the possibility of an open and protracted war.
Specifically, lawmakers fought over whether the measure should include a "sunset" provision, whether it should be limited in geographic scope, whether it should repeal either of the previous AUMFs, and whether it should permit the presence of ground troops (and if so, under what conditions).
The bill never reached the House or Senate floors for debate.
While the administration and members of Congress continue to call for an updated AUMF, the measure has taken a backseat to other initiatives, in large part because the administration says it doesn't need the AUMF to do what it has already been doing for more than a year.
"It's my understanding that we currently have all the authorities that we need to prosecute the campaign against ISIL," Dunford said at Tuesday's hearing. "But I absolutely believe that a clear and unequivocal statement of support for the men and women that are prosecuting the campaign and our allies from their elected officials would be absolutely helpful."
Helpful, but not critical -- and this lack of urgency is felt both in the White House and on Capitol Hill.
Sen. Bob Corker, R-Tennessee, chairman of the Foreign Relations Committee, suggested in a recent interview with Politico
that it would be imprudent for Congress to bring the controversial bill to a vote without an obvious need to do so.
"To bring up something that highlights a divide over that and maybe makes it appear as if the nation is divided over (ISIS)?" asked Corker. "It doesn't make a lot of sense to me."
But not all lawmakers have given up on the AUMF. Last month, Sens. Tim Kaine, D-Virginia, and Jeff Flake, R-Arizona, introduced their own draft proposal in June, and have continued to push for debate on the issue.
In an op-ed in Time Magazine
last month, the two senators called on Congress to galvanize behind the effort.
"In the aftermath of the horrible Friday the 13th attacks in Paris, many members of Congress quickly took the opportunity to blast the Obama administration's failure to appropriately counter ISIS in Iraq, Syria and beyond," they wrote. "It is fair game to challenge the administration's strategy, but these critiques miss an important point: Congress has abdicated its fundamental duty to debate, vote on and shape the extent of the current war on ISIS."
Debate, they add, would serve multiple purposes: It would force the administration to lay out a clear strategy, show American unity and "vindicate the Constitutional role of Congress in making the sober decision about when military force is necessary."
White House spokesman Josh Earnest made a similar argument to reporters on Monday.
"For more than a year, Congress has been AWOL on their responsibility to pass an Authorization to Use Military Force," he said, adding that Congress "must stop using the fact that these issues are difficult as an excuse for doing nothing."