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LOUISVILLE, Ky. -- Sen. Rand Paul (R-Ky.) will be at Minority Leader Mitch McConnell's side Monday in a seven-stop fly-around of Kentucky, seeking to boost turnout for McConnell's bid for a sixth term.

Make no mistake, however: Paul has his own stake in Tuesday's election. Although he's not up for election himself, the freshman senator is hoping to flip control of the state House to Republicans. It would make history, as this is the last Southern legislative chamber in Democratic control, and it has been this way since 1921.

More important, a new GOP majority in the Kentucky state House would revive the chances of changing a state law so that the libertarian-leaning senator could run for both president and his Senate seat in 2016. The state Senate, controlled by Republicans, passed a bill that would allow him to file for both offices but it died when House Democrats declined to take up the legislation.

With a margin of 54 to 46 in the state House favoring Democrats, Republicans here had higher hopes early in the year of winning, but privately some strategists in each camp give an edge to Democrats, whose candidates appear to be better prepared.

Still, some Democrats worry that if turnout is down across the state, or if the marquee Senate race breaks heavily for McConnell over Democrat Alison Lundergan Grimes, Republicans could sweep enough seats to claim the state House, too.

At Saturday's Democratic unity event in Lexington, several Kentucky Democrats made a point to remind voters of what is at stake beyond the Senate race, citing the legislation Paul is seeking to pass.

Paul is considering a court challenge if the law is not changed, citing other states that allow a candidate to run for two offices simultaneously. Delaware and Connecticut elected Joseph R. Biden Jr. and Joseph I. Lieberman to additional Senate terms as they were also the vice presidential nominees in 2008 and 2000, respectively. For now, Paul just wants state law changed.

"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," he told CNN earlier this year.

Such a situation could force Paul's presidential and senatorial ambitions to collide, prompting a situation in which he would run for president and not seek reelection to his Senate seat.

Other senators have been able to run for president, stumble in the primaries and withdraw, then file for reelection that same year. But that's because those states had late filing deadlines, something that is not the case in Kentucky.

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Rand Paul, not just McConnell, has a big stake in Kentuckys election