In the New York Times Magazine, Matt Bai suggests it is "an ominous sign, historically speaking, for a majority party" when "the president's own approval ratings fell below 50 percent":
[President Obama] continued to go out and shake his head disbelievingly at "the culture of Washington," which to the Democrats in the House sounded as if he were saying that his own party was the problem, as if somehow the Democratic majorities in Congress hadn't managed to navigate the bulk of his ambitious agenda past a blockade of Republican vessels, their ship shredded by cannon fire. And all this while the president's own approval ratings fell below 50 percent -- an ominous sign, historically speaking, for a majority party...
Just about every strategist of either party in Washington will tell you that the best indicator of whether the voters are growing less skeptical -- and, thus, of whether Democrats can survive the November elections intact -- can be found in the president's approval rating. There is a political theorem that illustrates this, supported by data from past elections and often repeated by Democrats now, and it goes like this: If the president's approval rating is over 50 percent in the fall, then his party will suffer only moderately. If his rating is under 50 percent, however, then the pounding at the polls is likely to be a memorable one.
I'm not sure why Bai thinks Obama's approval numbers are so ominous. Using USA Today's presidential approval tracker, I made this chart showing approval ratings to this point in each of the last seven presidencies:
Obama's approval trajectory (in purple) is tightly clustered with five of the last seven presidents. Only two of those seven -- George H.W. Bush and George W. Bush -- had significantly higher approval ratings at this point, and neither is an especially compelling counter-example: Bush 43's approval ratings were artificially inflated by 9/11, and Bush 41 was not re-elected. It's not clear that there's anything ominous about Obama's standing at this point.
If Bai is instead referring to the fortunes of the president's party in midterm elections under unified government, then there are only three relevant first-term examples in the contemporary era: Carter (1977-1978), Clinton (1993-1994), and Bush 43 (2001-June 2002). Of those, Democrats suffered moderate damage in 1978 with Carter around 50 percent; the Republicans won a landslide victory in 1994 with Clinton in the mid-40s; and Republicans picked up seats in 2002 when Bush's approval ratings were still extremely high.
Finally, if Bai is referring to midterm elections more generally, I'm not sure what makes 50 percent so magical. The president's approval ratings are an important factor, as this Nate Silver graph shows, but it's not clear that it matters whether Obama is slightly below 50 percent or not -- he's likely to lose seats either way (as most presidents do):
In reality, other factors such as slow jobs growth and the generic ballot are far more ominous for Democrats than Obama's approval rating.
[Note: The text of this post was revised.]