The Republican Party has the House of Representatives locked up due to gerrymandering until some core constituency departs.
Well mostly no and a little yes on your comment.
No, its not all because of gerrymandering that the R's have a majority in the US House. Its that the R's have a natural advantage in the race for the US House majority. Their voters are more spread out geographically than the Dems votes are. 16 out of the last 20 years the R's have head the US House Majority and 4 of them when the Dem had he US House Majority were because Bush W. was hated in 2006 and he GOP had a bad year electorally in 2008.
Yes, the Dems would have more seats in the US House because of GOP gerrymandering but not enough for a Dem US House Majority if the map was neutral(no gerrymandering.)