It's not impossible at all. If there were no "faithless" Democrat electors, and only Obama and McCain got electoral votes, the House would have to select McCain. No eligible candidate having gotten a majority of the electoral college votes, the House would have to select the President, per the XIIth amendment.
...The person having the greatest number of votes for President, shall be the President, if such number be a majority of the whole number of Electors appointed; and if no person have such majority, then from the persons having the highest numbers not exceeding three on the list of those voted for as President, the House of Representatives shall choose immediately, by ballot, the President. But in choosing the President, the votes shall be taken by states, the representation from each state having one vote; a quorum for this purpose shall consist of a member or members from two-thirds of the states, and a majority of all the states shall be necessary to a choice.
Nothing in the XXth amendment changes any of that.
The House is not nearly so divided by states as it is by sheer numbers. So voting by states makes that selection less "painfull" than it otherwise might be. But as I've said repeatedly, I expect at least one "faithless" elector, to provide a Democrat candidate for the House to chose,"just in case".
The 12th Amendment applies only if one of the candidates did not get a majority of the electoral votes. Obama got 365 electoral votes, well over the 279 majority. So it's the 20th Amendment that matters from here on out, and that doesn't contain the restriction on who may be selected president.