Kay Hagan made a meteoric rise from the State Senate to the US Senate two years ago, thanks to a strong campaign but also in no small part to a great political climate for Democrats. As her party's image has worsened in the last year so has her approval rating and now just 29% of voters in the state approve of the job she's doing with 42% disapproving.
90% of the voters who disapprove of Hagan's performance are opposed to the Democratic health care plan, indicating that issue may be driving her unpopularity. In a state where a majority are opposed to it a rise in her disapproval numbers was probably inevitable.
Hagan has pretty solid numbers with Democrats at a 49/19 spread but faces strong disapproval from Republicans (5/72) and independents (21/48).
North Carolina's Senators are really in the same bag politically- they're not that well defined personally with the voters so their fortunes are more inclined to rise and fall with the popularity of their parties. Right now for Richard Burr that's a good thing- he got elected in a Republican year and now he gets to stand for reelection in a Republican year.
Hagan won in a Democratic year and her popularity has declined with voters turning away from her party. She'd probably lose if she had to run for reelection this year- just as Burr would have lost in 2006 or 2008- but things may be back in good shape for her party by 2014 just as they were for Burr's by 2010. Impossible at this point to say what her future holds.
Hagan's full numbers here