It's a lie. Here are some articles discussing the Republican reaction to the 1960 election:
http://www.salon.com/politics/feature/2000/11/10/nixon/index.html
http://slate.msn.com/code/PressBox/PressBox.asp?Show=11/9/2000&idMessage=6459
http://slate.msn.com/historylesson/00-10-16/historylesson.asp
There is a book referenced in the Slate articles, 'Courthouse Over White House: Chicago and the Presidential Election of 1960', by Edmund Kallina.
It's in the collection (on loan) of my local university library; I've put in a recall to get it back. I expect it to arrive in 1-2 weeks.
In the meantime, if anybody has any further information on this, I'd appreciate it if they'd forward it to me.
Thanks,
Barry