The vote could ultimately provide Cheney with an opening among conservatives, as the far-right wing of the GOP seems largely opposed to intervention and, on most issues, Enzi has a strong conservative record.
But while Enzi maintained in a statement that he would appraise the evidence before deciding, he did seem to lean against military action.
“While I am not on the Foreign Relations, Armed Services, or Intelligence committees, I will be reviewing their findings and the testimony and evaluating the case President Obama lays out before the American people," he said.
“I am also reviewing the proposals for authorizing the President to act on Syria, though so far, I haven’t seen any reason to enter a war and risk American lives when there is no clearly defined national security interest and allies have not been cultivated," he added.
Cheney's choice to launch a primary challenge against Enzi baffled establishment Republicans in Washington and Wyoming, as the senator has a largely conservative voting record.
Her opposition to military engagement in Syria came as somewhat of a surprise as well, as the daughter of hawkish former Vice President Dick Cheney has previously defended the Iraq War and ran a national security organization called Keep America Safe.