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.

The Bluegrass State has a filing deadline in mid- to late January every year for federal and state offices, and under the new national Republican primary calendar for 2016, the earliest caucus and primary states aren't likely to begin until early February. At the time of Kentucky's filing deadline, Paul will most likely not have competed in a single primary, so he won't be certain whether he is likely to receive the nomination.

Kentucky law would forbid him from filing to run for both president and Senate, although some local experts wonder if Paul could test the situation in the courts by simply not filing to compete in Kentucky for president while filing for the Senate. If that were upheld in the courts, he would compete in the other 49 states for president but cede the voters of his home state -- which traditionally has a very late presidential primary.

It's unclear whether the state courts would side with him in such a case, and Paul has made clear he'd prefer not to deal with the issue in the courts.

Even if the state House flips, Democratic Gov. Steve Beshear has one more year in office, and he could veto the legislation. Still, at a local union rally Saturday evening in Louisville, several Democrats whispered their fear that a GOP-controlled legislature would use the Paul legislation as a bargaining chip in negotiations with a governor seeking legacy items.

All of that makes Monday's fly-around an intriguing trip, not just for McConnell, but also Paul.

Coincidentally, the campaign will end in Bowling Green -- the freshman senator's home town.