(CNN) -

Two longtime members of Congress who went into Tuesday with their political fates hanging in the balance appear to have survived intra-party challenges, one with the help of the other party.

In Mississippi, six-term U.S. Sen. Thad Cochran held off tea party-backed challenger Chris McDaniel in a race marred by name-calling, mudslinging, allegations of cheating and a break-in at a nursing home where Cochran's bedridden wife lives.

In New York, U.S. Rep. Charlie Rangel, who was first elected in 1971, claimed victory in what he says is his last race, looking like he'll survive a second straight narrow victory against the same opponent he faced two years ago when he barely kept his political career alive.

"I want each one of you to go home and know that this was your victory," he told supporters. "This is your congressman and you can rest assured that all I will be doing is thinking about you and bringing these resources home."

But Rangel's challenger, state Sen. Adriano Espaillat, wasn't conceding early Wednesday.

Democrats come out in GOP contest

In Mississippi, McDaniel called out Cochran for mobilizing Democrats to vote in the GOP primary.

"There is something a bit unusual about a Republican primary decided by liberal Democrats," the state senator told supporters. "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."

Mississippi has no recount provisions in its election laws. The only challenge to election results must go through the courts.

And McDaniel hinted that's a possibility late Tuesday.

"We were right tonight. We were right tonight," he said. "Now it's our job to make sure that the sanctity of the vote is upheld. We have to be absolutely certain that the Republican primary was won by Republican voters."

Mississippi law allows anyone to vote in the runoff, meaning Democrats could go to the polls as long as they hadn't voted in the Democratic primary and didn't plan to vote for their party's candidate in the general election. By CNN's count, about 55,000 more people voted Tuesday than in the primary two weeks ago.

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

They actively reminded voters of the senator's work to secure federal funds for programs such as Head Start and certain medical centers in the state.

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

Conservative groups supportive of McDaniel dispatched volunteers to observe poll workers to see if they were turning away those who already showed up in the Democratic primary.

But those efforts mobilized groups such as the NAACP, which sent out its own volunteers to look for any signs of voter intimidation or interference.

In his victory speech, Cochran seemed to at least wink at the crossover voters, thanking supporters for getting them and his supporters to the polls.

"You are the ones who helped reach all the voters, make sure that they knew that they were important to this election because it's a group effort, it's not a solo," he told a victory celebration in Jackson. "And so we all have a right to be proud of our state tonight. Thank you for this wonderful honor and wonderful challenge that lies ahead."

McDaniel outpolled Cochran by about 1,400 votes in the June 3 primary but was forced into a runoff when he failed to cross the 50% threshold to win outright.

Rangel's last dance?

Rangel had said win or lose this race was his last campaign.

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

Rangel, the former chairman of the tax-writing House Committee on Ways and Means, was forced to step down from that post in 2010, and the House censured him for ethics violations later that year.

Just as damaging for Rangel was the redrawing of New York's 13th Congressional District after the 2010 election -- from a Harlem-based, African-American-dominated district to one that now has a Hispanic majority, thanks to shedding parts of Harlem and adding other neighborhoods in northern Manhattan and parts of the Bronx.