Gallup, similarly, went from four points Democratic to one point Republican. And the 47 percent who identify as Republicans or Republican leaners is also one of the highest numbers since the mid-2000s.
(A third pollster, NBC/Wall Street Journal, showed no real change post-election.)
Going back through history, this isn't really surprising. Post-election party identification tends to tilt a little more toward the winners than it did prior to the election. Everyone likes -- or, perhaps more aptly, wants to feel like -- a winner once the results are tallied. So maybe the "independent" who just happens to always vote for Republicans suddenly claims to be officially on the red team.
Here's how that looks, courtesy of Gallup polling and the inimitable Philip Bump:
The only year in which this was not the case was in 2010, when party ID post-election was static, despite massive GOP gains. After the 1994, 1998, 2002 and 2006 midterms, though, that trend was intact, to varying extents (some of which, like the shifts in said election, were not terribly significant).
The bad news for the GOP, though: It doesn't usually last. The only real lasting change among all the years listed above was in 1994, when the Republican Revolution wrested control of Congress from Democrats for the first time in decades and effectively ended the long-standing "Conservative Coalition" between Republicans and conservative Southern Democrats.
The GOP does have some hope to retain its post-election gains this time around, though, especially given the Democratic brand has lost its longstanding superiority in the minds of Americans. If that continues, we might continue to see the two parties close to parity when it comes to party identification.
But even then, we've still got a very closely divided electorate. And, as mentioned above, plenty of those so-called "independents" are actually Independents In Name Only (IINOs).