The White House's hawkish rhetoric, according to Rogers, is "going to mean ... a more difficult road for him" to avoid taking military action in Syria.
U.S. forces are expected to begin missile strikes against military targets in Syria in the coming days, in retaliation to the reported use of chemical weapons by forces loyal to embattled President Bashar Assad.
The White House has warned that use of those weapons would cross a so-called "red line," triggering an armed response from U.S. and NATO forces.
U.S. warships are already in station in the Mediterranean, off the Syrian coastline, awaiting orders from Washington.
A fifth Arleigh Burke-class Navy destroyer, armed with long-range Tomahawk cruise missiles, has reportedly been deployed to the waters off the Syrian coastline.
As U.S. military forces in the region await the order to attack from Washington, lawmakers on Capitol Hill are mounting fierce opposition to taking action in Syria.
Sen. Rand PaulRand PaulConquering Trump returns to conservative summit Rand Paul rejects label of 'Trump's most loyal stooge' GOP healthcare plans push health savings account expansion MORE (R-Ky.) said Wednesday that the strikes would not serve any U.S. national security interests.
"The war in Syria has no clear national security connection to the United States, and victory by either side will not necessarily bring in to power people friendly to the United States,” Paul said.
Sen. James InhofeJames InhofeA guide to the committees: Senate GOP considers ways to ‘modernize’ endangered species law GOP bill would eliminate Consumer Financial Protection Bureau MORE (R-Okla.) echoed Rogers's claims that the White House's rhetoric has put U.S. armed forces in an intractable situation regarding Syria.
"No red line should have been drawn without the strategy and funding to support it," he said in a statement Wednesday.
Despite the White House's call to action, the Pentagon simply cannot afford to carry out any kind of operation in Syria, due to the fiscal restraints put on the U.S. military under sequestration, Inhofe added.
"Our troops are stretched thin, the defense budget has been slashed to historic levels, and we are facing an unprecedented time of unrest across the Middle East," according to the Oklahoma Republican.