In April 2011, the idea of running for Congress was still an April Fools’ Day joke for Kellie A. Greene, an Oswego native who was living in Arizona but was thinking about moving back home.

She had met that spring with a party chairman in the congressional district to gauge his interest in her candidacy. There was none; the party already had its candidate, she recalls being told. Matthew A. Doheny had run in 2010 and earned the loyalty of the GOP brass.

And yet here she is, just days before the GOP primary on Tuesday, running a campaign against Mr. Doheny that has defied, by turns, expectations, typical political logic, and Republican Party officials.

“Have you read the Constitution?” Ms. Greene said. “Does it say anything in there about the Republican Party picking a candidate? It’s not in there. It’s supposed to be the will of the people.”

A joke among friends has now turned into a long-shot candidacy, one that’s short on traditional politics and campaign funds, while long on gumption and optimism. Add a heavy dose of very conservative politics, and you have Kellie Greene, a recent graduate of seminary school and Sackets Harbor resident who, like many of the constituents she hopes to represent, has burned through her savings, carries a large debt load and has struggled economically in the recession.

If she can beat Mr. Doheny in a low-turnout election that will attract only a distillation of the conservative Republican base, could she beat Mr. Owens in November? Doheny supporters believe she can do neither. She believes she can do both with a low-key, low-turnout race.

Ms. Greene got involved in tea party politics in 2004 after meeting Sen. John McCain, an Arizona Republican, at a meet-and-greet there.

She worked as a logistics consultant, but the recession hit her hard. In 2011, after eight years in Arizona, she decided to move back to the north country, with political ambitions still lingering and poor job prospects. She landed what she thought was a dream job at New York Air Brake.

But her employment there was short-lived, which helped press her toward a candidacy. She couldn’t specify why she left Air Brake after three weeks in October; she signed a confidentiality agreement, she said.

Soon after her departure, she started laying the foundations for her run for Congress, despite the rejections from the GOP. She started emailing local conservative activists and former supporters of Douglas L. Hoffman, a tea party candidate who was on the Conservative Party line in the 2009 and 2010 races and had fallings-out of his own with the Republican Party.

Her supporters are a combination of people. There’s the subset of tea party-minded folks who are at odds with the institutional GOP.

They’re also the people who will never vote for Mr. Doheny, because they think he’s too moderate. Ms. Greene, a self-described “far-right conservative,” has suggested that federal employees shouldn’t have the right to unionize, that President Obama wasn’t born in the United States and that social welfare programs like Medicare and Medicaid might be unconstitutional, though too many people depend on them to get rid of them.

And there are those who find her candidacy refreshingly lacking in the accoutrements of typical politicians. Unlike Mr. Doheny and Mr. Owens, Ms. Greene doesn’t have much money of her own. She has between $15,001 and $30,000 in credit card debt, plus student loan debt between $250,001 and $500,000. Her fundraising coffers are almost as bare. She said that she’s paid many of her campaign expenses with credit, because she doesn’t have an income of her own.

Ever the nontraditional candidate, Ms. Greene counts this as a positive: She can relate to north country voters who have struggled in the recession.

After graduating from Fuller Theological Seminary in Phoenix in June, Ms. Greene said she hopes to enter the ministry. That’s a backup plan, of course. Few prognosticators share her view that she has a 50-50 shot against Mr. Doheny. No matter.

“If I didn’t think there was a chance, I wouldn’t have gotten in,” she said. “If I didn’t think there was a chance, I wouldn’t still be in.”

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