So how long until [Democrats] can start talking about taking back the [U.S.] House?
It will happen on the watch of next Republican U.S. president with two elected terms.
It's certainly not impossible (and obviously eventually Democrats are going to win back the House), but there are enough wealthy, exurban districts that are never going to elect a Democrat because they want a politician who is going to keep their taxes low, and now Democrats seem to have burned all of the bridges that they had left in socially conservative districts that were open (at least for a period) to their economic messages. It's a tough path (just as the GOP has a tough path in the EC right now).
I actually think waiting for enough suburbs to flip is the best strategy. The former Blue Dog districts generally gave Romney >60%, so they aren't coming back even if the next Dem president improved 10% with rural whites. They are currently in the same position as the GOP in 1960 when it comes to the South, having broken through in the cities and inner suburbs and fought to a draw in VA and FL but still getting crushed everywhere else. There's cause for hope, but the revolution's still 15-30 years away downballot. The big question now is whether they get an early assist from a reverse LBJ character. Don't discount the possibility of white collar suburbs completely freaking out after a Trump/Cruz nomination or worse, general election win. The Denver/NOVA effect will reach into some surprising places in a Trump/Cruz midterm, even in the cultural South.
Actually the opposite is probably true. As someone actually from the "cultural South" (whatever that is). Trump is playing the best with the wedges of voters you could imagine Democrats winning again. But as Obama drove them to Trump, Obama democrats aren't going to win them back. Trump's base in the south is likely not even going to vote in the GOP primary's. It is also the groups that would be most open to Democrats. But you got it completely wrong about Obama democrats attracting them. In fact they are driving them more toward the GOP. Trump's base is cultural regressives that don't know or care much about economics. They aren't for the most part Southern Republicans in the party sense ie they aren't Economic conservatives/neoliberals.
There is this myth around here that the entire South is going to follow the Virginia model. The Virginia model is unique. Virginia's growth in the last decade has been the consequence of the growth of government in DC effecting the NOVA suburbs. Of course those whose livelyhoods are dependent on big government aren't going to be voting for those advocating that we shrink government.
Another problem is liberals pretending push and pull factors exist. People leave the Northern Blue states for the Sun Belt mainly because of better economies/lower taxes. Obama Democrats or worse Sanders Democrats campaigning for massively higher taxes won't play.
Blue Dogs died out because people got tired of their dog and pony show. As the Democrats drifted left culturally, the Blue Dogs held on to power by running one way in their districts and voting another way in DC. People got tired of that.