It's not impossible if the polls are just way off in one consistent way: whites.
ohio pennsylvania wisconsin michigan all have somewhat similar demographics (76-79% white) Throw in even whiter states iowa 85% or new hampshire 91%. Obama beat romney in minnesota, wisconsin, michigan, ohio, and iowa all with 49-51% of the vote. Romney ranged 45-48%. New hampshire was 52-46.
If trump was going to win, he has to do it on the backbone of the white vote, and he absolutely must flip one of those longstanding democratic laregly-white-but-not-completely-white rustbelt states (WI, MI, PA).
Here's a map I think generous to Trump. If clinton wins ANY of the remaining uncolored states, she wins
The Republicans were hoping to make grounds in other demographics since the white population is declining -- I am not going to look it up, but I think bush had like 44% of hispanics in 2000 and now romney had like ~30%. If the white vote goes 60% for trump, 78*.6 = 46.8.
Clinton probably won't do as well as obama, so the Republican arithmetic of saying "We can't only win with the white vote anymore" may not be true IFF trump does great with whites. Romney had 59% of the white vote, mccain had 55, kerry vs bush had george w with 58. The analysis was that they weren't going to get better than Romney, and it just wasn't enough and soon definitely won't be enough with demographic trends. But if Trump can reel in a reliable 46% of the vote or so, it may be able to beat clinton with a few votes here and there from other groups.
The problem is that MN/WI/MI/PA have all been democratic since 1992. They are white, but democrat. A good example is WI, the rcp aggregate polls in wisconsin is like 46.7 clinton and 41.3 trump. In the primaries, it was all trump/cruz, meaning the voters were completely for the very conservative or nonstandard republican sideshow. One wouldn't imagine a +5 poll swing, but it is possible if a lot of white people show up no one expected. A state like minnesota where Rubio won, or New Hampshire where the moderates were closer, is a lot less likely to flip.