Adam Serwer compares the popular vote to House seats won in various states:
After Republicans swept into power in state legislatures in 2010, the GOP gerrymandered key states, redrawing House district boundaries to favor Republicans. In Pennsylvania, Democratic candidates received half of the votes in House contests, but Republicans will claim about three quarters of the congressional seats. The same is true in North Carolina. More than half the voters in that state voted for Democratic representation, yet Republicans will fill about 70 percent of the seats. Democrats drew more votes in Michigan than Republicans, but they'll take only 5 out of the state's 14 congressional seats.
But Bernstein says gerrymandering was less important than the above chart would suggest:
Political scientist Eric McGhee ran the numbers and discovered that Democrats probably would have done better, but not much better, using the old districts. If it’s not gerrymanders, what is it? Probably a combination of incumbency helping keep any majority party in the House in place, plus inefficient distribution of where Democrats live. As McGhee says, Democrats “?‘waste’ votes on huge margins [in cities], when the party could put many of those votes to better use in marginal seats.”
The Republican gerrymander following the 2010 census has given them a permanent tailwind of about six seats, and they'll keep this for the rest of the decade. Combine that with the incumbency effect, and Democrats are unlikely to regain the majority unless they win about 52 percent of the popular vote.