Always an unlikely scenario, but considering Trump's uphill road, one worth considering. If Clinton wins CO, PA, and VA, for example, the best Trump can do is the narrow road to a tie via NH/NV.
Setting aside elector / party-switching shenanigans for the moment, let's consider how a pure party-line vote in the House would be expected to go. Remember that each state gets one vote.
Obviously, given the Republicans' advantage in the House (and that the Republicans have a lot of Plains/Mountain West states in their back pockets), Trump is heavily favored there. Going by Cook's ratings, they already have 23 of the required 26 states locked down; barring a Democratic wave (which is unlikely in the event of a EC tie), they have these states:
(The states with 30% shading are those where a single representative abstaining or switching could cause the state to deadlock; in Utah, this would require Mia Love to lose, as well.)
They'd need three more states to hit 26. Obvious candidates are:
Florida: they'd need to win a single competitive race, with FL-02 or FL-07 likely possibilities.
Alaska: hold the single seat here.
Montana: hold the single seat here.
Virginia: win a single competitive race; VA-05 or VA-10 would do the trick.
Michigan and Arizona are also quite doable, and Wisconsin and Colorado are also within reach. Iowa and Nevada are a bit of a stretch, but by that point they'd have a clear majority.
TL;DR: If it goes to the House, Republicans will have a majority of states unless there's a huge disconnect between Presidential and Congressional voting.
Of course, the big question is, would it come down to a party-line vote? Could a faithless elector put a third option on the table that could attract enough Republican support to force multiple ballots? If so, who? If it's not a mass movement, are there enough individual House members with the power to deadlock a state and enough antipathy for Trump to do it? The ones that can are shaded light blue above (plus AK, MT, AZ, WI, CO, NV, & IA, should they win those).
And, entering the realm of fantasy, how about a Veep-like scenario where the House deliberately deadlocks so that Pence gets to act as President? This assumes, of course, that the Republicans keep the Senate; if they don't I can't imagine the House deliberately throwing the acting Presidency to Kaine / Warren / whomever.
