We've had electronic voting here for a few years now, and it's going fine, really. But then we're not the gargantuan monster of a body politic that the US is.
It would *probably* be fine here, too, though elections law in most states is really, really itchy about any possible tampering (and, as it stands, ballot tampering and fraud are both super, super rare here). One main obstacle (beyond simple mistrust) is that it isn't the federal government but rather the individual
states who set election standards. This makes the system wildly uneven, as some states run perfectly fine elections (my own, for instance) and then other places it's a total amphetamine parrotshow (Ohio, Florida).
So, if some states decide to go electronic, this is going to bother the other states (how can we trust those inept Ohio-ans, after all?) and, even if all
states were to do it, there wouldn't be a uniform system. Hence, nobody would trust what anybody else was doing.
At least with paper ballots you've got actual, physical evidence of voting. It's a pain in the ass, yeah, but it's hard to get more reliable than that. You know, barring the eternal danger of morons.