Many Democrats, too, are pressing for actions like creating a no-fly zone and trying to bring war crimes charges against the Syrian leader.
The calls are coming from many of the same lawmakers in both parties who for years urged President Barack Obama to do more to arm Syrian rebel groups and to strike the Assad regime, and now say that it's Trump's turn to act to remove Assad from power.
"I don't think there is a future with Bashar al-Assad in existence," Republican Rep. Adam Kinzinger of Illinois said on CNN's "New Day." "That is something that this administration, frankly, like the last one I think failed to do -- they did in words but not in deeds — this administration is going to have to come to that reality or this problem is sadly only going to continue and get worse."
On Tuesday, the Trump administration blamed Syria's attack on the Obama administration's failure to act against Assad. But at a news conference Wednesday, President Donald Trump said he is now responsible
for the situation, and suggested he was considering taking additional action.
"I will tell you that attack on children yesterday had a big impact on me, big impact," Trump said from the White House Rose Garden. "And I have that flexibility. And it's very, very possible, and I will tell you it's already happened that my attitude toward Syria and Assad has changed very much."
US Ambassador to the United Nations Nikki Haley also suggested Wednesday
at a UN meeting that the US could be "compelled to take our own action."
The statements earned praise from Arizona Sen. John McCain, who has been critical of the Trump administration's actions in Russia. McCain also defended Trump for blaming the attack on his predecessor.
"Think those were excellent words," McCain said when asked about Trump's statement.
"They did chemical attacks," he continued. "Barack Obama did worse than nothing. He said he was going to do something and then didn't. And that clearly gave Bashar Assad license to kill again."
But the comments from Trump and Haley were a shift from a week ago, when Secretary of State Rex Tillerson said the Syrian people would determine Assad's fate.
Sen. Marco Rubio of Florida said Tillerson's remarks could have given Assad motivation to launch the latest attack.
"My belief that if you're Bashar al-Assad and you read that it is no longer a priority of the United States to have you removed from power, I believe that that is an incentive to act with impunity," Rubio said at a news conference.
McCain and Sen. Lindsey Graham of South Carolina met with Tillerson for an hour at the State Department on Tuesday, and McCain said Tillerson was being misinterpreted.
"He said to me he realizes we've got to take action against these elements that are committing war crimes as we speak," McCain said.
Graham told CNN the Trump administration needs to make clear what its policy is when it comes to Assad.
"I'd be a disaster if it's a policy change, as bad as drawing the red line," Graham said.
Trump's comments even got some begrudging praise from Democrats.
"I'm pleased to see the president come away from the position that he was adopting mere days ago when he was making the point that Assad is a fact on the ground, sort of validating Assad's presence," Democratic Rep. Jim Himes of Connecticut told CNN's Wolf Blitzer.
For many Democrats, Tuesday's chemical attack was the latest evidence that a safe zone is needed in Syria to protect civilians.
"I think we should establish some kind of a safe zone in Syria where this humanitarian aid can be delivered to the Syrian people and with military protection for the safe zones so that, if anybody tries to mess with it, they will regret it," Virginia Sen. Tim Kaine said on CNN's "New Day."
Kaine was one of a group of Democrats who were also pushing the Obama administration to take similar action against Assad. But Kaine dismissed Trump's accusations that Obama could be blamed for the chemical attack.
"He's commander in chief. And when something happens and he tries to blame President Obama, give me a break," Kaine said. "And remember, when President Trump was just Donald J. Trump back then, he was urging President Obama not to do anything in Syria."
Not all members of Congress condemned Assad. Speaking on CNN's "At This Hour" with Kate Bolduan, Rep. Thomas Massie, a Kentucky Republican, told the host that he didn't think the Syrian leader launched the attack
, and that further intervention by the US government may aggravate the situation.
"Frankly, I don't think Assad would have done that," Massie said. "It does not serve his interests."