First, there are some differences between the 2012 race and the WaPo polling, which I have highlighted in yellow. Not all of these differences are Dems vs GOP, but rather, differences is amount. For example, Rhode Island has no surprises in their choice--Democrats. However, in 2012 Obama won Rhode Island by 27 points, and currently, Hillary is polling at a 10 point lead over Trump. Similarly, in 2012, Romney won Utah by a whopping 47%, but Trump only has an 11 point lead in this WaPo poll. Earlier polling showed his lead at 20 points.
Second, depending on the quality of this WaPo poll, it shows a reversal in a few states, like Mississippi, Arizona, & Iowa. On the one hand, Clinton's 1 point lead in Arizona is within the margin of error, so somewhat meaningless. But on the other hand, Romney won Arizona by 9 points in 2012. Other polling shows a similarly tight race as the WaPo poll, showing Trump with just a 1 point lead. What is more curious is Mississippi, where WaPo shows Clinton with a 3 point lead, and Iowa, which shows Trump with a 4 point lead. Both of these would represent reversals from 2012. I can perhaps buy the Iowa switch--I'm far more skeptical about a Mississippi switch to Democrats. However, earlier polling has already shown Trump and Clinton tied in Mississippi--in 2012, Romney won here by 11 points. Perhaps this GOP stronghold is turning purple?!
Third, there are also a few significant differences in today's WaPo results and earlier polling, although only one is a "switch," Ohio--earlier polling gave Clinton an average of a 4 point lead, while today's WaPo results give Trump a 3 point lead. These results would be within the margin of error, so the differences are largely uninteresting, but similarly, unhelpful in predicting a winner, other than to say, "it's likely to be close." Two states, Colorado and Wisconsin, had Clinton with a 10 point lead in earlier polls, but today's results give her only a 2 point lead. The latter results puts it in the margin of error, so could be a significantly tightening rate there.
Just for funzies, let's use the WaPo results as a blueprint, and see what it would produce in terms of an electoral result (neither Texas nor DC were in this poll--for the sake of argument, let's give Texas to Trump, and DC to Clinton--polling averages give Trump an 8 point lead in Texas). First, if we use it "as is," ignoring margin of error, and leaving out Georgia and North Carolina, where polling has a dead heat (0), Clinton gets 325 electoral votes, Trump with 182--a landslide for Clinton. Second, let's only use states where candidates have a 5 point or more lead--That gives Clinton 224, and Trump 158. At the 5-point cutoff, Clinton doesn't garner enough electoral votes to reach the required 270, although, with a 66 point advantage, we still have a reasonably likely Clinton win. In this scenario, she only needs a couple of the states that Obama won in 2012, like Florida+Pennsylvania. Trump's path is far more difficult--he would need to win most of these 11 states. For example, if he lost both Florida and Pennsylvania, he only gets to 265 electoral votes. Or, if we combine a 2012 Obama with with earlier pro-Clinton polling, say, if Trump loses Ohio, Michigan, Wisconsin, and Colorado, Clinton wins. In all, a Trump win is still a statistical possibility, but the path forward for Clinton continues to be far more mathematically obvious.