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Some Republicans believe the freshman congressman, Harvard graduate and Army veteran is their best chance at taking down Pryor. Cotton easily won his 2012 race and is a favorite of a number of Washington-based conservative groups. But Cotton has made no signals about whether or not he'll run for the Senate — or even said whether he's considering it.

The deep-pocketed, fiscally conservative Club for Growth and Tea Party-affiliated FreedomWorks both backed him in his 2012 primary and are already spending against Pryor, making him their first target of the 2014 election cycle.