“Can you really have equal application of federal law if someone like Paul Ryan or Joe Lieberman can run for two offices but in Kentucky you would be disallowed?” Paul said. “It seems like it might not be equal application of the law to do that. But that means involving a court, and I don’t think we’ve made a decision on that. I think the easier way is to clarify the law.”

Another potential presidential candidate, Republican Sen. Marco Rubio of Florida, has said he wouldn’t seek to run for his Senate seat in 2016 if he campaigns for president.