If you want to understand how destructive the 2010 and 2014 midterm elections were to the long-term downballot prospects of the Democratic party, all you need to do is look at this chart via Pew's terrific Fact Tank site.
In 2009, Republicans controlled both chambers in just 14 state legislatures. Six years later, they had total control in more than double that number. And that's not even the full, bad story for Democrats. Look at their numbers. In 2009, Democrats had full control in 27 state legislatures; by 2015 that number was down to 11, the lowest ebb for total Democratic control since, at least, 1978.
That massive disparity in state legislative control has all sorts of effects from the obvious (control of the decennial redistricting process) to the less so (a wider bench to groom future stars). And, Democrats don't have all that much time to turn things around before the effects of their losses in 2010 and 2014 become even more entrenched.
There are three elections -- 2016, 2018 and 2020 -- before the next round of national redistricting. If Democrats can't use the next six years to reverse their losses of the past six years, they could see the party drawn into semi-permanent (nothing is totally permanent in politics) minority status in the House of Representatives. The Democratic National Committee has identified reversing the party's massive losses at the state legislative level as a major priority going forward but the questions remains how much they can actually do about it.
Part of the reason Republicans have gained over 900 state legislative seats since Obama became president is that they have a very well-funded infrastructure that focuses only on winning state legislative chambers. Democrats, of course, have their own state legislative arm but the major donors that tend to finance these things are less engaged on the Democratic side than the Republican one.
Democrats' best hope is that a national political environment like the ones they endured in 2010 and 2014 doesn't repeat itself in 2016 (very unlikely), 2018 (iffy depending on which party controls the White House) or 2020 (impossible to know this far out). And that they can convince some of their big donors to give to a less-sexy-but-no-less-important cause than a presidential or Senate race.
It's a difficult task, having dug such a huge hole. And it's Republicans trump card amid shifting demographics that could severely complicate their chances of winning the White House over the decade or two.