Mitch McConnell's Republican primary challenger may be getting plenty of Tea Party support in his uphill campaign against the Senate minority leader, but that doesn't mean he sees himself as a Tea Party candidate.

"I'm not positioning myself as a Tea Party guy. I'm running as a Republican in a Republican primary," Bevin said Thursday on "The Daily Rundown."

Republican Senate candidate Matt Bevin, who is running against Kentucky Sen. Mitch McConnell, joins Daily Rundown guest host Luke Russert to discuss his campaign.

He bristled at the label, even though he's been supported by Tea Party-aligned groups, including the Madison Project, and even though he acknowledged he might be ideologically in sync with them.

"I've never been a member of a Tea Party. I never went to any Tea Party meetings, although I am fiscally very much in like mind, and grateful for and appreciative of the support of anybody no matter what group they might be part of," the wealthy Louisville businessman said.

Instead, Bevin declared that his race against McConnell is motivated by what he sees as a lack of leadership from the GOP leader, both on foreign policy and health care.

McConnell has yet to announce whether he supports military action in Syria -- the only member of party leadership not to do so -- and Bevin hit McConnell for failing to decide whether he supports President Obama's request for congressional authorization for action against Assad, which has been supported by House Speaker John Boehner and House Majority Leader Eric Cantor.

"I'd question whether he's taken any position frankly, and that's part of my issue with him -- his actual lack of leadership on any number of fronts."

Bevin said his position, though is clear -- he's opposed to any military action, aligning himself with the party's libertarian wing.

"I would be adamantly, adamantly opposed to any intervention militarily in Syria at this time because we have no business being there,” he said. “What would be the purpose? We've made it very clear we don't intend for there to be regime change, and yet we're going to launch missiles into a country, rearrange their infrastructure, kill people, many of them will be innocent people, for what purpose? What is the military purpose? What is the end goal? What are we looking to accomplish? There's absolutely no end game in mind."

And while Bevin has been supportive of Utah Sen. Mike Lee, who's pushing for a defunding of the president's health care plan before its Oct. 1 implementation, the GOP challenger said that doesn't mean he wants it pushed through at the cost of shuttering the government.

"What Mike Lee has said, and what I agree with, is the idea that everything should be funded in the continuing resolution -- except Obamacare. The CR should be passed, minus the funding of this," said Bevin.

Instead, he said Republicans should "call [Obama's] bluff" and force him to veto a bill without the health care funding -- already an impossibility to get through a Democratic-controlled Senate.

"I don't think it's wise to shut down the government. I'm not advocating that," said Bevin. "I truly believe he would blink on this, I really do. I think it would be unadvisable to force this down the American people's throat."

While Bevin may eschew the Tea Party label, his comments come as another outside group is pressuring McConnell also to blink on his vote on government funding. The Senate Conservatives Fund, started by now-Heritage President and former Sen. Jim DeMint, announced it was going up with a $340,000 television buy Sept. 6-17 on network and cable TV in the Bluegrass State.

"McConnell’s the Senate Republican leader, but he refuses to lead on defunding Obamacare. What good is a leader like that?" the ad asks.

SCF has named McConnell a top target for 2014, and have left the door open to backing Bevin.

Bevin still faces long odds against McConnell, who has already spent heavily against his challenger and released his own internal poll showing him with a 47-point lead.

A key part of McConnell's attack is branding him as "Bailout Bevin," criticizing money his family's bell foundry business received from the state of Connecticut after it was destroyed in a fire.

Bevin said the correlation was a "very, very different instance" from McConnell's own vote for the first TARP bailout in 2008.

"The benefit to this business was almost negligible. It was a $100,000 forgivable grant for which I’m personally liable. If I don't create 12 permanent jobs, keep them permanently there, then I personally am responsible to pay it back," said Bevin. "There's no correlation whatsoever to taking money and pouring it into the pockets of companies that then, in turn, spend hundreds of thousands of dollars funding Mitch McConnell's campaign."

Whoever emerges from the pricey Kentucky slugfest -- with nine months still to go before next May's primary -- will have another competitive contest against Democrat Alison Lundergan Grimes.