"I think our main goal is ISIL. And I don't know that we have a, quote, 'responsibility' in Syria after that. And I think the president is being commendably cautious here about being involved in the middle of a Syrian civil war. It's at the minimum a three-sided conflict and probably a lot more than that," Cole, an ally of House Speaker John Boehner (R-Ohio), told MSNBC's Chuck Todd.
Earlier in the interview, Cole also stressed that Obama should seek approval from Congress before taking any "extensive military action" against the Islamic State.
"I don't think the president should engage in extensive military action beyond what's allowed under the War Powers Act, without going to Congress," he said. "I think it's important politicly, and it's important for the world to understand that when we deploy force, we're doing it as a country and not in a partisan manner, that we genuinely are united. So I think the elements of a strategy are there."
Obama spoke at a White House press briefing on Thursday and said his administration was preparing a "range of options" for dealing with the Islamic State.
"Look, the president's made it clear, and I think appropriate, that we're talking about airstrikes at some point. We're talking about special operators. We're talking about, you know, aid and training for people on the ground. And we're talking about alliances in the region, which I think are going to be not easy to construct, but pretty doable since nobody on the ground, even our enemies, don't like ISIL," Cole told Todd.
Calls for a U.S. response to the group have grown since the gruesome beheading of James Foley, an American journalist who was kidnapped in Syria two years ago.
The United Kingdom raised its own terror threat level to "severe" on Friday in light of developments in Iraq and Syria.