In the last couple of presidential elections states which the Republicans had hoped to turn in to swing states such as Pennsylvania, Wisconsin, and Michigan remained blue. The two major swing states in the Bush years, Ohio and Florida, both went to Obama, along with some former red states such as Virginia. Looking at the electoral map, about the only large state (in terms of population and electoral votes) which remained firmly in Republican hands was Texas. Without Texas it would be impossible for Republicans to find any path to victory in the electoral college as long as current partisan divisions persist.
Republicans are losing outside of the south due to a combination of factors including holding unpopular, extremist positions and due to demographics. The same demographic trends can also be seen in Texas where white, non-Hispanic voters currently make up less than 45 percent of the voters. Real Clear Politics has a report on how Democrats are attempting to become more competitive in Texas.
Democrats might still not be able to win Texas in 2016 but if they could just be competitive and force Republicans to campaign there it would put them at quite a disadvantage. If Democrats could win some victories in the state government, they might also be able to reverse some of the gerrymandering and increase their chances of retaking control of the House in the next decade (if they don’t manage to do so before then due to the declining support for Republicans).