WASHINGTON — For all its horror, the beheading of an American journalist in Syria appears unlikely to change lawmakers’ minds about military intervention against Islamic State extremists. It’s equally unclear whether the Obama administration will be asking them to back a new U.S. approach.

President Barack Obama said the United States wouldn’t scale back its military posture in Iraq in response to James Foley’s killing. But he offered no specifics Wednesday about what new steps he might take to protect additional captives and other Americans, and ward off what he described as the al-Qaida offshoot’s genocidal ambitions.

The initial response from members of Congress was mixed, reflecting the divide of the American people. While all decried Foley’s death, hawks, particularly Republicans, continued to assail the Obama administration’s limited airstrikes in Iraq and its refusal to target Islamic State bases in neighboring Syria. The president’s supporters voiced support for the current, cautious intervention in Iraq. No tea partiers or dovish Democrats who have cautioned against military action publicly changed position.

“The president’s rhetoric was excellent, but he didn’t outline steps to stop the slaughter,” Sen. John McCain, R-Ariz., one of Obama’s harshest foreign policy critics, said in a telephone interview. “The strategy should be to launch all-out air attacks in Iraq and Syria to defeat ISIL,” he said, using an alternative acronym for the Sunni militants.