(CNN) As President Donald Trump assesses how to respond to the alleged chemical attack in Syria that killed and maimed dozens of civilians, lawmakers disagreed Monday what an appropriate response should be and whether Trump needed their authorization before acting.

"I think we need to take some surgical military strikes against Syria," said Republican Sen. Bob Corker of Tennessee, who chairs the influential Foreign Relations Committee. "Something for a heavy price to be paid."

Democratic Sen. Chris Murphy of Connecticut warned against it.

"Let's be clear, these pinprick strikes have not worked," said Murphy, who sits on Foreign Relations. "The President tried that a year ago and it seemed to make the situation worse, not better."

Republican Sen. Mike Rounds of South Dakota, a member of the Armed Services Committee, was among those who said Trump has the authority to act now.

"In a case like this, where you have determined chemical weapons are being deployed," Rounds told CNN, "we have recognized that the President does have the ability to respond in short order."

Democratic Sen. Ben Cardin of Maryland, a senior member on Foreign Relations, said the US needs to go the diplomatic route and work with the international community to build a case against Syrian President Bashar al-Assad.

"We need to work with the United Nations and hold President Assad accountable for his war crimes," Cardin said.

Several Syrian activist groups on Saturday reported the attack, which took place in a rebel-held suburb of Damascus. The groups said deadly gas was dropped in barrel bombs from helicopters. Gruesome and emotional images of injured and dying victims have played repeatedly on television and online since. The Syrian government has denied the allegations.

Speaking at a Cabinet meeting Monday at the White House, Trump vowed he would have a response within the next two days. "We cannot allow atrocities like that," he said.

After a similar attack a year ago, Trump ordered the firing of scores of cruise missiles at Syrian forces.

Immediately after last week's attack, Sen. John McCain, the Arizona Republican who's the chairman of the Armed Services Committee and supports a robust US military presence in Syria, blasted Trump and said he had "emboldened" Assad when he said last week that he wanted to pull American forces out of the country.

McCain's House counterpart, Texas Republican Mac Thornberry, called it a "mistake" for Trump to want to leave Syria at this stage.

"I think the notion that we would leave Syria is -- was a mistake, because we haven't finished destroying ISIS, and because people like Iran and Russia see a vacuum created when the US leaves into which they will run," he told CNN.

GOP Sen. Roger Wicker of Mississippi, who is also on the Armed Services Committee, agreed and said the US should not be "slaves to a timeline."

"I don't think the job is done in Syria, and I think we ought to stay until we get the results we need," Wicker added.

Republican Sen. Ron Johnson of Wisconsin cautioned that the US can't depart from Syria because it would "yield that to Iran and Russia."

"I think we have to respond," Johnson said. "But what I don't want to do is telegraph the response. If you're going to respond, respond. Do it quickly and effectively. Make Assad pay a price for that kind of heinous crime."

New Authorization for Use of Military Force?

Aside from what immediate military and diplomatic actions the US might take, Congress is struggling more broadly with how -- or if -- to update its Authorizations for the Use of Military Force for the war on terror, which were passed shortly after the 9/11 attacks.

Past efforts to renew them have collapsed under the competing demands of bipartisan lawmakers who want to place restrictions on the military missions and bipartisan lawmakers who want to give the commander in chief the widest latitude to go after terrorists, which they think resides in the existing authorities.

"The AUMF we're operating under now passed the week after September 11," said Sen. Angus King, a Maine independent who caucuses with the Democrats. "No amount of creative lawyering, in my view, can stretch it to cover intervention in Syria."

Corker said he believes he has found the "sweet spot" between those demands, and a new Authorization for Use of Military Force will be considered in his committee later this month. Senators and aides are keeping the details of the emerging compromise private, so it's difficult to assess if they have something that can pass.

Corker said he hopes details will be made public Thursday.

"We've kind of seen an outline of something that I think has been pretty thoughtful," said Johnson, a member of Foreign Relations, who was reluctant to discuss details before Corker unveiled them.

Senators said it was improbable that a new Authorization for Use of Military Force could be completed before Trump might take immediate action against Syria but that if it turns into a lengthy conflict a new authorization might be needed to approve the deployment.

"If they are surgical in nature, no," said Corker. "If we are going to go against the regime on any kind of sustained basis, there has to be an AUMF."

Murphy said Trump should not act without congressional approval, but he acknowledged the President might anyhow.

"The President doesn't have the authority to take military action," said Murphy, who is heavily involved in trying to rewrite the Authorization for Use of Military Force. "There is zero legal justification to take strikes against the Syrian regime when there is not an attack pending against the United States."

Wicker warned that he did not think a new Authorization for Use of Military Force had good odds to pass, putting them at less than 50-50.

"There are some people who actually don't believe the War Powers Act is even constitutional. They feel it limits the commander in chief in a way that's not conducive to do national security in an emergency. And there are other people who just don't want to authorize any use of military force," he said.

"A new authorization is not at the top of my list of priorities," Wicker added.