It seems pretty likely that Rand Paul will attempt to run for the Republican nomination in 2016, but unlike other Presidential and Vice Presidential candidates, he won't be able to run for his Senate seat and the Presidency at the same time, due to Kentucky state law. The law varies from state to state. "Several members of recent presidential tickets have essentially hedged their political bets by running for re-election while simultaneously pursuing higher office." (e.g Paul Ryan ran for both his House seat and as the Republican VP nominee, Joe Biden also ran for Delaware's Senate seat, and as the Democratic vice-presidential nominee in 2008, and Joe Lieberman ran for the Connecticut senate seat and lost his bid for the Vice Presidency with Al Gore in an extremely close election in 2000. (In 2008 Barak Obama's senate seat in Illinois was not up for election that year ). The issue also came up in 1960 when Lyndon Johnson faced the same dilemma, and the Texas legislature passed a statue allowing him to run for both races. Taking a nod from history, a bill was introduced into Kentucky's state house to change the state law, and while it passed the Republican controlled Senate, the Democratic controlled House never considered it and Brian Wilkerson, a press aide for the House Speaker noted to reporters: ""In Kentucky, you ought to run for one office at a time "The speaker's thoughts haven't changed on that." The Kentucky state governor Steve Beshear (D) has no plans to reconvene the state house to reconsider the proposed bill.
And there are Republicans who agree in a self serving way, including Marco Rubio (Florida - R, which incidentally had no such limit). "I think by and large, when you choose to do something as big as that, you've really got to be focused on that and not have an exit strategy," Rubio said during an April 2 appearance on the Hugh Hewitt radio show.
Overall, I think this is a good development, because it will force Rand Paul to decide if he's really serious about his Presidential run, and commit to it) and by having a "play-run" at the party's nomination, and attempt to impact the Republican nomination process. I'm pretty sure the Republican candidates who are supporting the current law in Kentucky are do so purely in their own self interest. And yes, I think other states should have such requirements limiting elected officials to one race.
In March, 2013 Nate Silver posted some detailed analysis on the chances for Ron Paul in 2016. Mr. Silver thinks Rand Paul is sincerely interested in expanding his base for any real chance at winning the nomination. And noted "But [Senator] Paul at least seems to demonstrate the interest in expanding his support beyond libertarian conservatives, something his father rarely did, and he will have three years to experiment with how to find the right formula. That doesn’t make him as likely a nominee as a more traditional candidate like Mr. Rubio, Jeb Bush or Representative Paul D. Ryan of Wisconsin. But his odds look better than the 20-to-1 numbers that some bookmakers have placed against him.