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Some Republicans, like the dovish Sen. Rand Paul (R-Kentucky), have outlined proposed authorizations of war against the extremist group ISIS that are even more narrow than the one President Barack Obama sent to Congress on Wednesday.

Some of the most hawkish Republicans, however — like Sens. Lindsey Graham (R-South Carolina) and John McCain (R-Arizona) — want to go further, giving the president with whom they disagree on nearly all matters foreign policy almost unlimited power to wage war.

“We are already seeing a clear divide between presidential hopefuls,” said Ian Bremmer, the president of the risk consulting firm Eurasia Group.

Welcome to Republicans’ 2016 war primary, one that will reveal many of their divisions on foreign policy heading into a free-for-all nominating process.

Among members of Congress thinking about a presidential run, there are the clear doves — like Paul, who released his own authorization of military force against ISIS last November. His proposed authorization that would limit the use of ground troops for rescue missions and intelligence gathering, and his authorization would expire one year after passage.

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Then there are the hawks, like Graham and Sen. Marco Rubio (R-Florida), who has said the authorization should leave open the possibility of sending U.S. troops into the fight.

Finally, there are the somewhere in-betweens — like Sen. Ted Cruz (R-Texas), who has suggested he’d like a broad campaign to destroy the group but has said Congress shouldn’t hand Obama a “blanket authorization.” He’s also said he wouldn’t support any legislation that would require political change in Iraq’s divided government.

“Rubio and Graham [support] strong action, while Paul snipes openly at them (well, particularly Rubio, since no one has yet determined that Graham has much hope),” Bremmer said in an email.

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“This will increase as the campaign develops. There’s going to be a widening divide in the party, which will prove important if Paul’s campaign gains any real traction,” Bremmer added.

Why these four senators matter

Amid the coming potential circus GOP primary with more than a dozen potential candidates, those four senators will be the only presidential hopefuls who will have the power to shape the authorization and and vote on it. The authorization will have to pass through various committees on which the senators sit — and eventually, the entire Congress will vote.

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Representatives for some governors with presidential ambitions — New Jersey’s Chris Christie, Wisconsin’s Scott Walker, Arkansas’ Mike Huckabee, and Florida’s Jeb Bush — didn’t respond to requests for comment. Neither did a spokesman for former Secretary of State Hillary Clinton.

But it is the four senators who will be in the spotlight during this politically charged debate. And if they make the wrong choice when it comes time to vote, it could loom large for their political careers and candidacies, as it did for Clinton’s 2008 campaign in the Democratic primary against Obama, when she faced substantial criticism for her vote to authorize the deeply unpopular Iraq war.

“Everyone wants to be seen as strong, as someone who can be a worthy steward of America's foreign policy as President, but will not want to come off as too eager to use increasing levels of force,” said Garrett Khoury, the director of research at The Eastern Project.

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Will Obama align with the hawks?

Graham and Rubio have pressed the case for U.S. ground troops to be a possible part of the equation toward defeating ISIS. Rubio on Tuesday told Fox News’ Megyn Kelly he thought the strategy should include a ground force made up of Arab armies and U.S. Special Forces. He also said he doesn’t think the AUMF (shorthand for the war authorization) should include geographic limitations — a suggestion to which the administration adhered, but one that places Rubio in a different camp than Paul.

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“Well, think about it this way: If you put a geographic limit on the authorization of the use of force, you’ve basically told ISIL where they can go to hide,” Rubio said in response to a question about Paul’s views.

“If you say, for example, you can only hit them in Iraq and Syria, they have every incentive now to move their operations and their training facilities to some other place that’s not included within it.”

The differences between Paul and Rubio could be on full display during hearings held by the Foreign Relations Committee, which will take the lead on shaping the bill. Both senators serve on that committee. Paul has been openly critical of his fellow senator and potential rival, taking to social media to blast some of his positions on foreign policy — including a difference of opinion over the Obama administration’s move to normalize relations with Cuba.

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Graham, meanwhile, also wants the authorization to reconcile with the possibility that the U.S. may need to fight multiple enemies in the region. That includes the forces of Syrian President Bashar al-Assad, who many analysts blame for fostering the rise of ISIS. He’s said it doesn’t make sense for the U.S. to train Syrian rebels to fight ISIS without the authority to go after Assad if he targets those rebels.

“It's certainly going to be a good fight,” Khoury said. “Obama will probably lean more towards the Rubio/Graham/McCain side of the argument, though, as he is going to want as much authority as possible for as long of a period as possible. If anything, he'll have more trouble restraining Graham and company than getting them to give him enough authority.”

Brett LoGiurato is the senior national political correspondent at Fusion, where he covers all things 2016. He'll give you everything you need to know about politics, with a healthy side of puns.