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For two Republican senators from the same state, Rand Paul and Mitch McConnell could not be more mismatched.

Senator Paul is a man in a hurry, with presidential stars in his eyes after a mere four years of serving Kentucky in Washington. The loquacious libertarian is a darling of young conservatives 鈥� a relaxed jeans-and-boots kind of guy.

Senator McConnell, after three patient decades in office, has finally reached his dream job of Senate majority leader. A man of few words, he鈥檚 from the establishment wing of the party. In Washington, he sometimes sports golden, presidential-seal cuff links.

鈥淚 don鈥檛 think any state has a more interesting pair of senators and a more influential pair of senators,鈥� says Al Cross, director of the Institute for Rural Journalism and Community Issues at the University of Kentucky in Lexington.

Kentucky is one place in America where a tea-party firebrand and a Republican from the governance wing amicably meet 鈥� though it's taken a recognition of mutual interests to make that happen. While their relationship could be dismissed as a political marriage of convenience, analysts say it's an example of how two people with different philosophies can come together once they get to know each other 鈥� the way members of Congress from different parties used to for much of the 20th century.

Five years ago, Paul and McConnell were on opposite sides of a political battle. But since then, they鈥檝e forged a symbiotic relationship that, Paul hopes, will prove particularly useful to him at a critical juncture this weekend.听

On Saturday afternoon, Paul met with Kentucky GOP leaders, and 鈥� with a valuable nod of approval from Senator McConnell 鈥� asked them to switch from a presidential primary to caucuses. That would enable him to run for both the Senate and the presidency without running afoul of state law that forbids a name from appearing twice on a ballot.

It鈥檚 a big ask, and questions about the idea abound. Doubters听worry about the logistical heavy lift, participation of voters, and risks to other party priorities at the self-serving request of one man.

鈥淧aul has a serious problem with the ballot law, and McConnell is helping him get around that,鈥� says Mr. Cross.

After overcoming earlier skepticism, McConnell鈥檚 approval of the idea, 鈥渕akes a lot of difference,鈥� says Cross. 鈥淧eople were looking to him for leadership and he鈥檚 provided it, and I think most of them will follow.鈥�

The big assist, which followed a Feb. 23 meeting between the two men, is another example of the political odd couple鈥檚 mutually beneficial relationship.

It was just 2010 when Kentucky鈥檚 senior senator was at serious odds with Paul, the ophthalmologist son of Ron Paul 鈥� a three-time presidential candidate with a faithful libertarian following. The younger Paul, backed by tea party supporters, was running for the US Senate, his first political office, against McConnell鈥檚 anointed choice, Kentucky Secretary of State Trey Grayson.

First, the McConnell machine tried to turn Paul out of the race by offering to back him for a state senate campaign, according to an . When that didn鈥檛 work, it was combat. Among other anti-Paul efforts, McConnell supporters set up a website, , that sought to document Paul鈥檚 鈥渞adical鈥� views, including support for marijuana legalization and opposition to the wars in Iraq and Afghanistan.

After Paul trounced Mr. Grayson by 23 points in the primary, McConnell pivoted and fully backed Paul for the general election. He couldn鈥檛 ignore the anti-Obama fervor and the appeal to young voters that Paul represented.听

Nothing illustrates that political lesson more than one October day when McConnell, stumping with Paul, was getting ready to emerge from the campaign bus. He saw the crowd of enthusiastic tea party supporters and realized he didn鈥檛 recognize many of their faces. McConnell had other things going that day, but cleared his calendar to spend the rest of the time with Paul.

The schedule change was 鈥渁 great testimony about McConnell鈥檚 exquisite sense of self preservation,鈥� says Cross. 鈥淗e could see that Paul was in the process of taking over the party that he was the titular leader of.听 If he wanted to remain the titular leader, he needed to get in touch with these people.鈥�

The McConnell-Paul relationship began as 鈥渇ormal and stiff,鈥� says Mike Shea, a lobbyist in Kentucky who started with McConnell as Jefferson County GOP chairman during McConnell鈥檚 first run for county office in 1977.听

But the relationship gradually improved, with McConnell continuing to extend support, including an assignment on the foreign relations committee to help round out Paul鈥檚 resume. Paul's isolationist positions have moderated somewhat, and he has even guided McConnell on domestic policy, resulting in a pilot program for industrial hemp to fill the void left by Kentucky's drop in tobacco farming.听

McConnell praised his colleague in Time鈥檚 April 23, 2014, issue listing the 100 most influential people. About the junior senator he wrote: 鈥淭he real secret to Rand鈥檚 rapid rise from a Bowling Green operating room to the center of American politics is his authenticity. It鈥檚 a trait that鈥檚 obvious to anyone who has seen him come out of a D.C. television studio in Ray-Bans and shorts, or hold the Senate floor for half a day to get answers from an imperious White House.听

鈥淪pend five minutes with Rand and it鈥檚 clear he doesn鈥檛 care what you look like or where you鈥檙e from. He鈥檚 beating the bushes for anyone who prizes liberty, and he鈥檚 forcing people to rethink the Republican Party.鈥�

That snippet appeared in the midst of McConnell鈥檚 own primary campaign battle last year against a tea party candidate, Matt Bevin. But Paul, who might have naturally backed Mr. Bevin, instead endorsed McConnell, helping him on to victory 鈥� and to that long-sought job of majority leader.

Paul also campaigned for other Republicans in more than 30 states, including for the 鈥渆stablishment鈥� candidate Sen. Pat Roberts of Kansas, whose incumbent bid was tottering.

In his first one-on-one newspaper interview after the November election and Republican wave, McConnell told the Lexington Herald-Leader that if Paul decides to run for president, 鈥渉e鈥檒l be able to count on me,鈥� adding that they have developed 鈥渁 very tight relationship.鈥�

鈥淢cConnell gets it. Their partnership is more than just convenience. Heck, their wives go shopping together,鈥� said Mr. Shea in an interview shortly after last year鈥檚 election. In 2010, the relationship 鈥渨as bound for the toilet,鈥� he said. 鈥淏ut both of them are too smart to toss it away. For Rand Paul, it could have been easy for someone with a lot of pride to say, 鈥楾he hell with you.鈥� 鈥澨�

Now Paul is counting on McConnell鈥檚 support for the caucus idea, along with letters from Rep. Thomas Massie (R) of Kentucky and Agricultural Commissioner James Comer, a gubernatorial candidate, to sway any doubters on the state GOP executive committee.

The majority leader's concerns were apparently assuaged by Paul's argument that the caucus would be a one-time event that would not affect other state races, that Paul would pay for it, and that, by moving up the date of the Kentucky's presidential selection process, it would give the state more clout, .听

This may well turn out to be McConnell鈥檚 last big favor for the junior senator, says Scott Lasley, a political science professor at Western Kentucky University and chairman of the Warren County Republican Party. If Paul decides to run for president, he鈥檒l be moving in a universe outside of McConnell鈥檚 solar system.

Others agree. True, McConnell will still be able to open some doors for contacts and donations, but a presidential campaign involves vastly different candidates, voters, and donors.听

鈥淚鈥檓 sure McConnell could share his lists and the like, but when you step back, a presidential race is so different,鈥� says Stuart Rothenberg, editor of the Rothenberg Political Report.

And the fight for the Republican nomination could well be determined in blue states, not red ones, Mr. Rothenberg points out.听

鈥淚 don鈥檛 know how much influence Mitch McConnell will have with primary voters in states like New York and California,鈥� he says.

Still, both Kentuckians have an interest in keeping the symbiosis going. McConnell may well need Paul鈥檚 help in dealing with Senate tea party renegades such as Ted Cruz (R) of Texas, who has presidential ambitions of his own. And as a presidential candidate, you never know when a Senate majority leader will come in handy.听

Ryan Alessi in Murray, Ky., contributed to this report.