Should the U.S. military engage in the Iraq crisis?

Mike Rogers: Terrorist safe haven being estab... 04:42

Democratic and Republican lawmakers all said on "Face the Nation" Sunday that the U.S. has a counter-terrorism mission in Iraq, but there's little agreement on the best way to continue ensure the nation's security.

House Intelligence Committee Chairman Mike Rogers, R-Mich., and Sens. Marco Rubio, R-Fla., and Barbara Boxer, D-Calif., all weighed in on the ongoing crisis in Iraq, where Sunni insurgents continue to capture territory in northern Iraq.

Marco Rubio: ISIS "more dangerous today than ... 06:48

"I think this is an urgent counter-terrorism matter. I know a lot has been talked about the future of Iraq itself as a country and that's a very legitimate issue that needs to be looked at, but for me this is not about nation-building, or imposing democracy -- this is a counter-terrorism risk that we need to nip in the bud," Rubio said. "It is my view that we will either deal with ISIS now or we will deal with them later. And later they are going to be stronger and harder to reach."

He argued the best way to fight the Islamic State of Iraq and Syria (ISIS) is to cut off their supply lines between Iraq and Syria, where the group has gained strength and recruits in recent years.

"Primarily, that involves air power," Rubio said, rejecting a suggestion from his colleague, Sen. Rand Paul, R-Ky., who wrote in the Wall Street Journal that U.S. air power could end up serving as an air force for Iranians aiding the government of Iraqi Prime Minister Nouri al-Maliki.

"I think that's quite an exaggeration. The truth of the matter is that if we do nothing, Iran is still going to be involved," Rubio said. "To do nothing and allow ISIS to establish a base of operation, like what al Qaeda had before Afghanistan, places us in a very dangerous position from a counterterrorism point of view, and puts Americans lives on the line down the road."

He did, however, say President Obama should not "unilaterally go out and announce to the world, 'These are the things that I'm not going to do.'"

A fellow Republican, Rogers said Secretary of State John Kerry should work to re-engage the U.S.'s Arab League partners during his trip to the Middle East this week. The relationship, he said, is "as damaged as I've ever seen it" because the U.S. has done little to intervene in the Syrian conflict.

"ISIS is as much a threat to their governments as it is to the Shia-led Maliki government, that's why they had been calling," Rogers said. "Remember, the decision not to be more robust in Syria seemed, well, it was easy to do because I don't think people understood the sheer size and pooling of the al Qaeda elements in the east. So when we walked away from that, they are very frustrated with us. Our Arab League partners are as frustrated and nervous about what happens next."

Rogers said that ISIS established "safe havens" in eastern Syria which allowed them to build up their forces, consolidate large swaths of land, recruit fighters and finance their activities. Arab League partners can help in both Syria and Iraq if the U.S. re-engages them, he argued.

In a separate interview with CBS' Norah O'Donnell that will air on "CBS This Morning" Monday, Mr. Obama defended his decision not to take a more active role in Syria in recent months by arming moderate rebels, which Rubio has called on him to do now.

"I think this notion that somehow there was this ready-made, moderate Syrian force that was able to defeat Assad is simply not true," the president said. "The notion that they were in a position suddenly to overturn not only Assad but also ruthless, highly trained jihadists if we just sent a few arms is a fantasy."

Obama: ISIS a "medium- and long-term" threat ... 03:04

He also said that the U.S. is not "just going to play whack-a-mole and send U.S. troops occupying various countries wherever these organizations pop up."

That stance drew a critical response from Rogers, who said, "this is in our national security interest. Bumper sticker phrases aren't gonna win this thing; we've gotta be dug in for the long haul because they're dug in for the long haul."

Barbara Boxer: The U.S. is never going back t... 03:44

But Democrats, many of whom staunchly opposed the 2003 invasion of Iraq, are likely to resist another major intervention in the country. Boxer, one of those anti-war Democrats, told O'Donnell that the current conflict is "an outgrowth of that bad policy the neo-cons got us in," and agrees with Obama that the U.S. will not reengage in a war in Iraq.

However, she added, "we do have a counter-terrorism mission, and I support that mission." She said the military advisers Mr. Obama has sent in to monitor the situation and assist Iraqi security forces are important for the U.S.

Boxer echoed the president in dismissing the idea that sending weapons into Syria might have curbed ISIS. She laid more of the blame with Iraqis for not forming a stronger, less sectarian government after the U.S. left.

"The Iraqis had their chance. They blew it, and I think right now, they've got to figure out if they can form an inclusive government," she said.

She also slammed former Vice President Dick Cheney for arguing in an op-ed that Mr. Obama has been consistently wrong on policy at the expense of many.

"That is sick," Boxer said, pointing instead to Cheney, former Secretary of State Condoleezza Rice and former Defense Secretary Donald Rumsfeld for the current situation.

Those who are calling for an active intervention are "like a nightmare come back to haunt me," Boxer said. "The American people don't want it; the president doesn't want it; the saner voices in the Senate and House don't want it."

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    Rebecca Kaplan covers Congress for CBS News.