The post Civil War years were times of great change for American politics. Between Abraham Lincoln's Vice President Andrew Johnson mismanaging the post war occupation in the South so badly and the public (northern) anger towards the Democrats (most confederate sympathizers were Democrat) the Republican party enjoyed political support higher than America has ever seen before or since the war.
As political parties or movements are prone to do though, they overplayed their hand and became corrupt. They took full advantage of the spoils system under the pretense of patriotism and installed their friends and family in what would seem non political positions (post office workers, sheriffs etc.)
They also 'waived the bloody shirt' whenever they could. This term was coined by the Democrats and basically meant they tried to whip up anger over the Civil War during rallies in the North and tried to direct that anger towards the Democrats since most southerners were Democrats. This strategy worked for a while after the war, but as the actual veterans of the war started to die out and the public became preoccupied with the industrial revolution, this strategy seemed stale and out of date. Kind of like the public now is tired of Vietnam dominating the tired debates of Congressional ex hippies and cold war soldiers.
Just like now we have crusty old politicians looking at the culture and cold war issues as the 'real' debate who refuse to address the real issues that face the country such as preventing another financial crisis, the crushing national debt or the country's over response to terrorism threats, those politicians of the 1870's and 1880's tended to spar over who could out Civil War one another and which side was responsible. The public, even in the south had moved on to more pressing issues such as what the governments role should be in managing the industrial revolution and whether there should be a safety net for citizens.
As the Democrats rose back to power, the Republicans declined. The political machines which were at the height of their power in the gilded age of the post reconstruction years gradually gave way to national parties with parties based more on ideas than the geography of their members. The national parties would become so entrenched in American politics that the presidency would be challenged only a handful of times by a non major party ticket. The only ready examples I can think of for credible third party runs are the Bull Moose party of Teddy Roosevelt and Ross Perot's run as an independent.
It makes me nostalgic for the days of the Whig, Liberty and Anti Mason parties.