and the chances of that happening are......?
Not unreasonable. The most likely method is by a local referendum. Once it gets put on the ballot, I think people will agree that it makes sense. The arguments are simple. Say for example, you love the Libertarian Party but hate the Democrats. Currently you would have to vote Republican to ensure that the Democrats don't get power. With IRV you would select your Libertarian Party candidate as your first choice and your Republican candidate as your second choice. In this way, your vote for the Libertarian Party couldn't be used to help the Democrats, since in each runoff the lowest scoring candidate gets dropped. If the first runoff gives the Republicans 50 votes, the Democrats 55, and the Libertarian Party 10 votes, since no party has a majority yet, another runoff must be performed. Then the second runoff might be 58 votes for the Republicans and 57 for the Democrats, giving the Republicans the office (your vote now becomes a Republican vote because your candidate was dropped).
Once enough states use it, there will gain momentum for a Constitutional amendment. It will be especially popular among Republicans because they remember how Ross Perot lost the election for George H. W. Bush. If Perot would not have run, Clinton probably would have never been the President.