It's a little disingenuous to say that there are 12 states "up for grabs". They are considered "competitive" because the margins of victory have been under 10 points, but in the 72 state elections in those 12 states in the last 6 presidential elections, the Dems have won 50 for a winning percentage of nearly seventy percent (69.44% to be precise). So until some of those states with narrow but persistent Democratic margins shift Red, the Democrats have a considerable advantage in the electoral college.
The problem with looking at the last six elections is that we don't really know how the current era is going to be considered.
There are some who seem to think that President Obama was a poor candidate dealt a bad hand, and that his four point win in 2012 suggests Democrats are favored to improve on the numbers in 2016.
My guess is that Obama's a good candidate, who had the benefit of running as an incumbent (whose party hadn't been in the White House long) under decent circumstances (Osama had a bullet in his head, the economy was recovering and Obama showed leadership in a national crisis just before the election) so his four point win doesn't suggest that the party is invincible. Since 1928, there's been a consistent trend of parties peaking and steadily declining, and right now it seems the Democrats peaked in 2008 (which doesn't mean they'll lose. Democrats peaked in 1936 and kept the White House for three further elections despite steady attrition.)
It may be that an era of Democratic domination of the presidency began in 1992.
I think we're more likely to be in an era of relative parity. The last six elections include four in which Democrats were naturally favored, and two in which a weak Republican still ended up getting reelected President (you could quibble on Gore winning the popular vote and Florida shenanigans, but it wouldn't have been an issue if he had been able to win the popular vote by four points.)
Looking at states Democrats won in the last six elections makes Wisconsin, which they won by less than half a point in 2000 and 2004, seem to be the equivalent of reliable blue states like Maryland and Massachusetts. I'm sure Republicans in December 1989 were happily looking at the electoral votes their party had won in the previous six elections.