What was the greatest number of faithless electors that the US experienced in voting for President in any historical election for the modern era (FDR--to present)? And how many faithless electors would Hillary Clinton need to win given she wins New Hampshire and Donald Trumps has already won Michigan?
Since 1912, the greatest number is one. In 1912, there were eight. The largest number ever was sixty-three, but that was because Horace Greeley died after the election but before the electoral college voted. The second greatest was thirty-two.
Source (Thanks, Jonno Downes.)
Hillary Clinton would need thirty-eight electors to switch to win (228 + 4 + 38 = 270). That wouldn't break the Greeley record, but is more than in any more normal year. And it would be the first time since 1912 that more than one elector switched.
It is unlikely but possible that if thirty-seven electors switched to Clinton, that she could win in the House of Representatives. Republicans would control the House delegations of more than the necessary twenty-six states, so it would take Republican votes. But we're already assuming that thirty-seven Republican electors would switch. Why not thirty Representatives too? Of course, if the House were to deadlock, the Vice-President selected by either the electors or the Senate (if the electors tie on VP too) would take over.
Thirty-eight is the reliable number. And is unlikely, as Republicans seem to be making their peace with the idea of President Trump.