Well, back to Rome. The even split between two parties is what crippled the Republic. There never was a one-party takeover like a modern dictatorship. The empire was founded as a cult of personality by individuals who, usually, stood outside of political parties...and even politics in general.
One party dominating isn't so unheard of, and has happened a few times in our own past. What we're seeing here is the classic death of a party. Usually, another will rise up to take its place... Or it'll be reformed. There are four instances in the 19th century where we pretty much see a single-party system for an election or two while one party implodes. The implosion is often because of extreme radicalization over whatever the issue is.
So what's happening now is as American as apple pie. The Republicans themselves are an upstart moderate party that was born out of the radicalization of the Whigs. The Democrats are an offshoot party that polarized around Jeffersonian politics.
The GOP and the Democrats are our longest lasting parties, but that's because they both cut their teeth on the slavery and Civil War issues. Something that we're still sort of recovering from, politically and geographically speaking. It's long overdue for one of the parties to collapse. This is why, for the large part, the Democrats have chosen such a bland centrist path. It's a survival strategy to prolong their existence.
What actually happens to political parties is what we're witnessing in the GOP now -- fragmentation, polarization, and a general loss of any sense of center. Normally, the party then fades away and is replaced.
Political types have been predicting the fall of the GOP since the 30's... And, if you weigh their candidates, you sort of see the shift in focus post-1936. The Republicans who have made the grade post-FDR era are all "raised on a shield," to keep the Roman parlance. Ike, Nixon, Reagan, Bush II (with Ford and Bush I riding coattails). Electing personalities and not fixers/doers (like LBJ, Carter, Clinton, and Obama) is another classic sign of a crippled party.
Now, the lines do blur. Nixon and Reagan billed themselves as fixers, and Clinton and Obama are certainly personalities. But, once in office, the differences were clear.