JACKSON, Mississippi (CNN) -

Rep. Charlie Rangel is claiming victory in his last dance.

The Democratic congressman from New York, who was first elected to the House of Representatives 44 years ago, appears to have survived a fierce primary challenge.

Rangel, who says this will be his last re-election campaign, will likely edge out state Sen. Adriano Espaillat, who came close to ousting Rangel in the Democratic primary two years ago. Espaillat did not concede Tuesday night.

Rangel was one of two four-decade veterans of Congress who avoided being ousted from office.

After a long and bitter fight, Sen. Thad Cochran of Mississippi will manage to fend off a serious tea party challenge in Tuesday's GOP Senate runoff, CNN projects, and move closer to a seventh term. In the primary, McDaniel edged out Cochran by less than 1,500 votes.

In a bizarre twist, it might be Democrats that helped push Cochran ahead at the finish line.

Along with Mississippi and New York, six other states held contests Tuesday.

Democrats likely swung GOP contest

To clinch the GOP nomination, Cochran's backers turned to Democrats, especially African-Americans who make up 37% of the state's population.

Cochran's supporters actively reminded voters of the senator's work to secure federal funds for programs relied upon by African-Americans, like Head Start and certain medical centers in the state.

It's the kind of message that Republicans barely tout these days, given the renewed focus on fiscal conservatism. But Cochran supporters viewed Democrats as key to their strategy to knock out McDaniel after the incumbent barely kept his reelection hopes alive in the primary.

Mississippi law allows anyone to vote in the runoff, meaning Democrats could go to the polls so long as they didn't vote in the Democratic primary and they don't plan to support their party's candidate in the general election.

But McDaniel and allies argued the tactic was a stretch, and he argued that a high Democratic turnout for Cochran would reveal the senator's true colors.

"I'm not concerned about them being African-American. I'm concerned about them being liberal," he told CNN. "That's always been my concern. If Senator Cochran is going to court liberal Democrats to save his seat, that's a good indication that he's abandoned conservatism in Mississippi."

As Cochran declared victory, McDaniel railed against Cochran's campaign tactic of stirring support among Democrats.

"There is something a bit unusual about a Republican primary decided by liberal Democrats," he said.

"So much for bold colors. So much for principles. I guess they can take some consolation that they did something tonight for once again compromising, for once again reaching across the aisle, for abandoning the conservative movement."

McDaniel added: "If it can happen here, it can happen anywhere. And that's why we will never stop fighting."

Mississippi law doesn't include provisions for election recounts. Any challenge to race results would have to go through the courts.

To make sure Democratic voters weren't voting illegally, conservative groups supportive of McDaniel dispatched volunteers to observe poll workers and whether they're turning away those who already showed up in the Democratic primary.

But that effort raised eyebrows from groups like the NAACP, which sent out its own volunteers to look for any signs of voter intimidation or interference.

Rangel's last dance

Win or lose, Rangel of New York says this is his last campaign.

The Korean War veteran, who was first elected to the House of Representatives 44 years ago, is trying keep from getting pushed out office by Espaillat, who came within around 1,100 votes of ousting Rangel in the Democratic primary two years ago.

"As we learned in 2012, every single vote needs to be counted in this race. Given the thousands of votes outstanding, the people of Upper Manhattan and The Bronx deserve a full accounting of every vote to achieve a complete and accurate tally in this race," Espaillat said in a statement in the early hours of Wednesday morning.