Incumbent Republican Richard Burr leads two potential leading Democratic challengers in this year’s U.S. Senate race in North Carolina. However, his numbers continue to display potential weakness.

A new Rasmussen Reports telephone survey of likely voters in North Carolina finds Burr ahead of Elaine Marshall 47% to 37%. Six percent (6%) favor another candidate, and 10% are undecided. That’s little changed since September.

Any incumbent who polls below 50% at this point in an election cycle is considered potentially vulnerable. It is striking to note that Burr remains below that 50% mark in a political environment that is very favorable for Republicans. If the political environment improves for Democrats between now and November, the incumbent could be facing a serious challenge. No incumbent has been reelected to the seat Burr holds since 1968.

The first-term Republican senator barely reaches the 50% mark in a match-up against former state Senator Cal Cunnignham. In that race, it’s Burr at 50% and Cunningham at 34%. Given that match-up, five percent (5%) like another candidate, and 11% are undecided.

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Burr leads both Democrats by wide margins among male voters. Marshall holds a seven-point lead over Burr among female voters, while Cunningham and Burr run even among this group.

Marshall runs slightly stronger than Cunningham among Democrats, but voters not affiliated with either party overwhelmingly prefer the Republican.

Last year, Democrats considered Burr one of the most vulnerable Republican incumbents gong into this fall’s election. But they’ve become less optimistic about a pickup in North Carolina with the continuing bad economy and the national mood swing over the health care plan that culminated in last week’s surprise GOP Senate win in Massachusetts.

North Carolina voters strongly opposed the health care plan in the September survey, and just 35% now think it’s even somewhat likely that Congress will be able to agree on a smaller, bipartisan health care plan this year. Fifty-six percent (56%) believe that Congress is not likely to pass such a plan. This is comparable to views nationally.

Nationally, 61% of voters say Congress should drop health care reform and focus on more immediate ways to improve the economy and create jobs.

In North Carolina, 61% of voters say the better way to create jobs is to cut taxes, but 16% say increased government spending is the better course.

Only six percent (6%) in North Carolina say the U.S. economy is good or excellent. Fifty-four percent (54%) view its condition as poor.

Twenty-six percent (26%) say the economy is getting better, but 46% think it’s getting worse. Nineteen percent (19%) say it’s staying the same.

Barack Obama narrowly carried North Carolina over John McCain 50% to 49% in November 2008, but he was the first Democrat to carry North Carolina in a presidential election since 1976. Forty-eight percent (48%) of North Carolina voters now approve of the job President Obama is doing. These findings are slightly better than Obama’s job approval ratings nationally in the Rasmussen Reports daily Presidential Tracking Poll.

Eighteen percent (18%) of Tar Heel voters have a very favorable opinion of Burr, who was first elected to the Senate in 2004. Twelve percent (12%) view him very unfavorably.

Marshall, the secretary of state since 1997 and the first woman elected to statewide office in North Carolina, is viewed very favorably by 13% and very unfavorably by 12%.

For Cunningham, very favorables total eight percent (8%) and very unfavorables (11%).

At this point in a campaign, Rasmussen Reports considers the number of people with a strong opinion more significant than the total favorable/unfavorable numbers.

In the wake of the December 25 attempt by a terrorist to blow up a U.S. airliner, 72% of North Carolina voters think it’s at least somewhat likely that there will be another terrorist attack this year in the United States. That number includes 32% who say it’s very likely.

Thirty-four percent (34%) say the United States is now safer than it was before the September 11, 2001 terrorist attacks, but 47% disagree.

Thirty-one percent (31%) give the government good or excellent marks for its handling of the Christmas Day terrorist incident, but 41% rate its performance as poor.

Seventy-eight percent (78%) favor the use of full-body scanners in airports.

Democratic Senate incumbents who currently trail their challengers include Harry Reid in Nevada, Michael Bennet in Colorado, Blanche Lincoln in Arkansas and Arlen Specter in Pennsylvania. Barbara Boxer from California, Evan Bayh of Indiana and Russ Feingold of Wisconsin find themselves in more competitive races than usual.

Republicans lead open-seat Senate races in Delaware, Florida, Kentucky, Missouri, New Hampshire, North Dakota and Ohio. Democrats lead in Connecticut, and the race is close in Illinois. A commentary by political analyst Larry Sabato, suggests that if the election were held today, “the (59-seat) Democratic majority in the Senate would be reduced to just 52 seats.”

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