Granted, 2010 was probably a worst-case picture for youth turnout; there wasn’t a competitive statewide contest and it was a bad year for Democrats. But nonwhite turnout also dropped, even beyond that caused by lower youth turnout. Combined, the consequences are potentially devastating for Democrats. Mitt Romney’s modest victory margin of 2 percentage points would have turned into a 10-point rout if the 2012 electorate had been as old and white as it was in 2010.

That’s a big problem for Ms. Hagan. She originally won her seat in 2008, when she won by a decisive 8 points. But her entire margin of victory came from voters under 30, who gave her a staggering 71 percent of their votes and represented about 17 percent of the electorate. If the voting public had been as old and white as it was in the 2010 midterms, Ms. Hagan’s share of the vote would have fallen beneath 50 percent; she still would have won, helped by a libertarian candidate, Chris Cole, who appeared to erode the vote for her Republican opponent.

To win such an old electorate in 2014, Ms. Hagan would need to retain nearly all of her support from six years ago. There are plenty of reasons to doubt her ability to do so. The 2008 election was extraordinary for Democrats, particularly among young voters. Between 2008 and 2012, President Obama lost more ground among younger voters than any other age group. Likewise, it seems hard to imagine that Ms. Hagan could hold 71 percent of young voters in 2014.

Ms. Hagan also outperformed President Obama among older, conservative white voters, many of whom are registered Democrats. She will certainly outperform Mr. Obama among older white voters once again. But they might be less likely to vote for federal Democrats with Mr. Obama in the White House. And Ms. Hagan might not benefit from a strong libertarian candidate this time.

Just one factor has turned in Ms. Hagan’s favor since 2008: She is now the incumbent. But there isn’t much evidence that Ms. Hagan is benefiting from incumbency. Her name recognition is low, and her job approval ratings are abysmal. Last week’s Upshot NYT/Kaiser Family Foundation polls showed Ms. Hagan with a 44 percent approval rating and just 42 percent of the vote in a head-to-head matchup with her likely Republican challenger, Thom Tillis. But these polls are of registered voters and assume a younger and more diverse electorate than the one Ms. Hagan will face in November. Ms. Hagan’s 2-point lead turned into a 3-point deficit among voters who said they would definitely vote.

Mr. Tillis might bail out Ms. Hagan by running a weak campaign. It wouldn’t be the first time that Republicans squandered an excellent opportunity against a vulnerable Democratic senator. But so far this cycle, off-year turnout and the president’s sagging ratings have prevented Democrats from matching Mr. Obama’s performance in 2012, even when Democrats have strong candidates, like Alex Sink (who lost a bid for a House seat in Florida), or weak opponents, like Ken Cuccinelli (who narrowly lost the governor’s race in Virginia).

Ms. Hagan’s road to victory is even more challenging. She’s far more dependent on young voters, and, unlike Florida’s 13th Congressional District or Virginia, North Carolina voted for Romney.