It's not only Democrats who worry about "drop-off voters" in 2014. Turnout patterns do hurt the party in non-presidential years, but Republicans are also focused on making sure a core group of libertarian-leaning potential supporters don't sit out key Senate races—or even support a third-party candidate. That could be the difference between recapturing the majority or not. So in the final weeks of the campaign, groups like the U.S. Chamber of Commerce are sending in an unusual closer.

"Rand Paul's turning out to be a good secret weapon this cycle," said Scott Reed, the senior political strategist for the Chamber, which recently ran an ad featuring Paul touting Republican Senate candidate Thom Tillis in North Carolina. Paul hasn't been a Tillis supporter for as long as the Chamber; while Reed's group was promoting Tillis during the GOP primary campaign, Paul had thrown in his lot with a fellow physician named Greg Brannon, who was running as a tea-party candidate.

But Tillis made it out of the primary to a fall general election ballot that includes Libertarian Sean Haugh, who happens to be getting more support in polls than the gap between Tillis and Democratic Sen. Kay Hagan. Reed believes that the libertarian-minded Paul's endorsement will help shore up enough of that support to close the gap in this and several other Senate races.

In recent weeks, Paul has spent time backing establishment candidates with appearances or similar ads in Alaska and Virginia—plus his home state of Kentucky—all of which have Libertarians grabbing small chunks of the vote in polls. Paul also has plans to visit Georgia (where candidates have to get over 50 percent of the vote to win) at the end of the month for Republican David Perdue, who shares a ballot with Libertarian Amanda Swafford, and he will stop in Kansas, where Republican Sen. Pat Roberts has lost conservative support to both independent Greg Orman and a Libertarian candidate in recent months.

Reed believes that Paul's influence could transform a number of races, that he can go into states where a Libertarian candidate is taking 6 to 7 percentage points and cut that number in half.

"We've analyzed these last few elections and recognized, in a number of these Senate races, Libertarians are drawing a lot of votes away from the pro-business candidates," said Reed. "As we looked at the landscape this cycle in Alaska, we thought Rand Paul would be the perfect messenger. We polled it, tested it, discovered that he's very popular with the Liberty caucus in Alaska, and put it on the air."

Reed says the Chamber has plans to use Paul in several other states during the final weeks before Election Day and had no trouble convincing him to cut ads for them in Alaska or North Carolina.

For the most part, the Kentuckian has required little arm-twisting when it comes to making house calls in states on the Senate's midterm map. Many of the competitive states, like Iowa and New Hampshire, are also useful destinations for a potential 2016 presidential candidate. A spokesman for RAND PAC, one of Paul's political committees, said the senator "believes in making the Republican Party bigger" and that he's become "one of the most in-demand surrogates" for the GOP.

It's made for a frustrating fall, though, for some of those Libertarian Senate candidates, especially given that Paul's father, Ron, was the 1988 Libertarian Party presidential nominee.

"I won't say surprised, but I was disappointed, obviously, and I think that a lot of other libertarian-leaning folks in Alaska were, too," Alaska Libertarian candidate Mark Fish said of the ad Paul cut for Republican Dan Sullivan. "It's not going to make a difference on them voting for Dan Sullivan; it's just further evidence of Rand Paul compromising on some of his principles."

So goes the divide between the "little L" libertarian Paul, and "big L" Libertarian candidates. Some of the candidates say they never expected Paul to come to their aid, but are nonetheless saddened to see him campaigning for establishment nominees.

Fish concedes that looking at the 2016 presidential field, Paul may provide his party's best shot at advancing its ideas from the White House—"the most libertarian with the best chance of winning," Fish says. Paul's presidential ambitions are not lost on the Libertarian candidates he's campaigning against.

"I've personally long ago made my peace with the fact that Rand Paul is running for president," said Haugh, of North Carolina. "It's to be expected. That's what he's got to do: try to neutralize or win over establishment opposition that he may have within the Republican Party."

Haugh, like many of these candidates, has had a long relationship with the Paul name. He's been voting a straight Libertarian ticket as long as he can remember, but in 2012 he registered as a Republican for a brief time to support state convention nominees aligned with Ron Paul's GOP presidential campaign. Asked whether he could picture the elder Paul canvassing for establishment candidates as his son has, Haugh sighed: "No, he really didn't do that sort of thing."

Swafford, the Georgia Libertarian, said the Paul name still carried some weight in her state party, but that many aren't sure where they stand on the younger Paul.

"Libertarian-leaning voters are still trying to ascertain where his thoughts are connected to his father," said Swafford. "Certainly Congressman Paul has a lot of influence with libertarian voters, much more influence certainly with Libertarian Party members than the younger Paul."

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