President Trump's warning that he could deploy the U.S. military if state and local officials aren't able to quell days of riots is facing skepticism and in some cases pushback from GOP senators.

Trump, speaking at the White House, said he would deploy the military — sparking a new wave of speculation that he could invoke the Insurrection Act, which would allow him to deploy active military troops to states and cities.

Sen. Lisa Murkowski (R-Alaska) warned against further militarization in response to the protests.

"I don't think militarization is the answer to the anxiety and fear, the distrust ... that we feel right now. It is not the response," she said.

Sen. Lindsey Graham (R-S.C.), a close Trump ally, said the law should be invoked as a "last resort."

"I don’t think the Pentagon’s keen on getting brought into this unless they absolutely have to. We need to restore order, but using active-duty military troops in circumstances like this is a fairly rare occurrence — so as a last resort," he told reporters.

Sen. John Thune (S.D.), the No. 2 Republican senator, told reporters he would "prefer that these things be handled by the state and local authorities. ... You want to de-escalate rather than escalate."

Sen. Tim Scott (R-S.C.) told reporters that talk of sending in the military was "premature," while Sen. John Cornyn (R-Texas), a member of GOP leadership, said that "ordinarily it's a local matter."

"Hopefully he won't do it, it won't be necessary," Cornyn said about Trump's remarks.

Asked if thought the president was floating the Insurrection Act, Cornyn added, "That would be one of the legal authorities he would depend on, but I think at this point that's hypothetical."

The Insurrection Act, passed in 1807, is a law that gives the president the power to deploy active military troops on U.S. soil. 

It was used in 1992 when the governor of California requested federal assistance in response to riots in Los Angeles but has not been used since then, according to Just Security.

But other GOP senators signaled that they would be more supportive of Trump taking further action if state and local officials are unable to prevent riots or looting.

Asked about Trump's "threat" to use the military, Sen. Ted Cruz (R-Texas) said it was an "interesting editorializing to use the word threat."

"The president has a responsibility to defend the country. And I'm glad the president is committing to acting swiftly," he said.

Sen. Ron Johnson (R-Wis.) said the federal government's main response should be investigating individuals involved in riots but that Trump's response could give governors "a little spine." 

"Hopefully, you know, the president talking that way will put a little spine in some of these governors that aren't calling out the National Guard to the extent that they need to to restore order," he said.