Trump will lose but the republican party will borrow heavily from the popular elements of his platform and completely reinvent itself, it will become more populist, pro-american, pro-middle class, significantly less socially conservative and it will make her very competitive. The Dems will not change, no one does while they are winning but they will lose in 2020 after which the Bernie's wing of the party will take over.
I honestly doubt that the grandpas running our country have the stomach to change ineffectivity. But this may be thee end of the Republicans.
Granny says it don't matter anyway... ... Jesus comin' purt soon... ... to rapture alla good people away... ... an den Hillary an' all her people... ... gonna have to figger out what to do.
The Republicans will retrench. It is what they've done the last few times it is what they will do now. Since they organized their last retrenchment around racism I would not be surprised to see them becoming much more misogynistic. As they become increasingly irrelevant I would not be surprised to see a third party, possibly a Green, become the second major party in the US. The Dems will evolve to become much more like Sanders as we see how well liberal programs work over conservatism and people become convinced that even more liberalism will work even better. I think the Republicans will eventually ally with the Dominionists, and become one of the small parties, like the Prohibitioists. The non-Trump factions are Dominionist now in practice.
The republicans (the people, not the establishment) have done something totally unprecedented and unexpected by nominating Trump with his liberal past, indifference to social conservativism and populist economic/foreign policy message. Yet you keep pretending that nothing has changed and they will keep doing what they had been doing before Trump... Wishful thinking at its best. The vacuum will be filled, Trump has demonstrated that there is a huge appetite in the US for his pro-working people, pro-middle class, anti-immigration platform (not dissimilar to Brexit). There will be a slew of new republican leaders promoting Trump's ideas without having Trump's personal baggage and controversies.. In four years the Republican party will be the populist, pro-working class party and it will be more than competitive with the Democratic party which represents the interests of the top 1% while paying lip service to minorities and the poor.
I do expect that the Republican Party is going to fade away after this; Trump is going to be a racist stain on their past no matter how they try to reinvent themselves, and Hispanics, Blacks, and possibly Asians if he does anything to alienate them in the next few months, aren't going to be voting Republican after this. By 2043, going at current rates, whites will be a minority in the US; the Republican Party quite literally can't survive that in its current form, or in any form, which means that it's expiration date is numbered in decades.
I don't expect it to collapse outright. I imagine that the Dems will go SocDem/socialist, the Libs will rise as a liberal/moderate conservative coalition while the Repubs will become a fascist party and remain a major player in (conservative) state politics while fading away nationally. This assumes we keep a plurality voting system. If we go proportional or preferential, the Dems and Repubs will probably remain players but they'll end up shrinking as their coalitions collapse in the face of electoral viability for minor parties.