The Republican establishment and conservative third-party groups are tussling yet again — this time in Kentucky’s 4th district.

In a crowded GOP primary to succeed retiring Rep. Geoff Davis (R), the local Republican establishment has split its support between state Rep. Alecia Webb-Edgington and Boone County Judge-Executive Gary Moore. Several outside tea-party-affiliated groups, and Sen. Rand Paul (R-Ky.), are backing Lewis County Judge-Executive Thomas Massie.

Unaligned Kentucky Republicans see momentum behind Massie. He has the most money being spent on his behalf — including $543,000 from a Texas-based super PAC reportedly funded by a wealthy college student — and the backing of FreedomWorks and the Club for Growth, which have both spent heavily on anti-
establishment candidates in recent Senate primaries.

“When I look at all these factors of low turnout, voters who don’t know the candidates very well, I don’t see how — if that super PAC spends twice as much as a single campaign — I don’t see how that doesn’t make Massie the favorite,” said former Kentucky Secretary of State Trey Grayson, who lost the 2010 Senate primary to Paul and is now the director of the Harvard University Institute of Politics.

Kentucky Republicans head to the polls Tuesday, and the sense among Bluegrass State insiders is that Massie has the upper hand, with Webb-Edgington close behind. But any of the three could squeak out a victory given the expected low turnout and the crowded field.

Though Webb-Edgington and Moore both have GOP establishment backing, that support breaks differently. Moore has pulled in establishment money from   U.S. Chamber of Commerce supporters and banking executives. Webb-Edgington has snagged the backing of popular Kentucky politicians, including Davis and former Sen. Jim Bunning (R). A Webb-Edgington campaign aide said the state Representative also has some tea party support.

“The people who want not-Massie appear to me to be all divided out between Moore and Webb-Edgington,” added one longtime Republican observer of Kentucky politics. “If it goes to Massie, I think the establishment will need to have a meeting and decide to be smarter the next time around.”

None of the top three contenders started with particularly high name identification, and earned media coverage is tough in a district split across a number of media markets. Candidate fundraising has been relatively even.

On May 2, Webb-Edgington had $110,000 in cash on hand, Moore had $137,000 and Massie had $136,000 in the bank, according to Federal Election Commission filings. That makes the super PAC buy for Massie all the more potent. That organization, Liberty for All Super PAC, is based in Texas.

“It would be very hard for me to see how Massie doesn’t win it” with the super PAC, said a GOP operative familiar with Kentucky. “The 4th is easily the center of the tea party universe in Kentucky … [and] if there is anywhere in America that is tea party central, that’s it.”

Those running against Massie hope to turn his outside support against him. The Texas-based super PAC “angered a lot of your rank-and-file Republicans” Moore campaign manager Jonathan Duke said. People are “put off that a libertarian from Texas is trying to buy a Congressional seat in Kentucky.”

But Grayson, who had the backing of the GOP establishment in his 2010 primary and experienced a similar dynamic, said it is unlikely to sway a lot of voters. Grayson said he polled on the issue of out-of-state money during his contentious primary against Paul, who had significant non-Kentucky fundraising, and it didn’t move the needle.

“I’m not sure the voters care too much about it,” he said.

Massie said he thought he had the edge and likened primary turnout in his race to the Grayson-Paul contest.

“I think our voters are the kind of folks that elected Rand Paul, who has endorsed me,” Massie said in an interview. “They’re the kind of folks who would show up in a tornado” to vote.

But some operatives in the state see Webb-Edgington as having a clearer path to victory. “In a seven-way primary, I gotta put my money on the woman,” one Republican said, noting she’ll be the only woman on the ballot.

Another complicating factor is the negative direct mail from candidates about each other and from super PACs about the candidates. “Anytime you’ve got three people in a race, it’s like walking into a metal room and shooting a gun,” the GOP observer of state politics said. “The bullet can ricochet.”

The winner of the GOP primary on Tuesday is almost certain to be the next Member of Congress.

Roll Call rates the race as Safe Republican.