1980: GOP overwhelmingly
1982: Dem barely
1984: GOP
1986: Dem
1988: GOP
1990: Dem barely
1992: Dem
1994: GOP overwhelmingly
1996: Dem
1998: Dem barely
2000: GOP barely
2002: GOP
2004: GOP
2006: Dem overwhelmingly
2008: Dem overwhelmingly
2010: GOP overwhelmingly
2012: Dem
It seems that neither party has had a monopoly on power as soon as each party gave up its "traditional" "moderate" bases of support.
Do you think that the era uninterrupted one-party (albeit superfluous at times) rule is over?
No -- not if one Party can entrench itself indefinitely through gerrymandering or (if possible) alteration of voting rights to the permanent advantage of the Party that enacts the alteration (yet to happen -- but if employers can control their employees' votes, such ensures one-Party rule indefinitely).