"In his own way, the hillbilly has a point"
Please bear with me through the following:
The motivation of the Republican Party in general and the current administration in particular to gain ever greater amounts of power - by whatever means possible and damn the consequences - is evidenced most recently in the Supreme Court's partisan appointment of George Bush Jr. as President, the attempt to recall California Governor Gray Davis, and the Ken Starr investigation and attempted impeachment of President Clinton.
That's from an article about the possibility of electronic voting systems being rigged. Apparently, as Diebold is the major manufacturer of said systems, and as several of their board members are Republicans, this is all a part of the VRWC to take over America, etc. etc.
Now, just because someone is wearing a triple-strength tinfoil hat doesn't mean that they couldn't be right about one or two things. Whether this is part of the VRWC or not I don't know; sometimes I just scan my instructions, and I might have missed the one concerning electronic voting.
However, the possibility exists that someone of any political leaning could modify these systems or the data they produce to change the results of an election. This is a non-partisan issue, so I'd suggest just ignoring those who try to make it one.
I don't know VerifiedVoting.org's political leanings, but their resolution - which you can sign - appears reasonable enough. (I can't get their online form to work, so I sent my information via the chat at the bottom of their contact page.)
The key to prevent abuse of these systems would appear to involve some kind of "Voter Verifiable Audit Trail." Without knowing the details of what experts in the field have developed, here's my suggestion:
Don't worry too much about whether the hardware or software is secure, just print out two copies of the person's vote. The voter verifies that both copies are accurate, takes one home with them, and drops the other in a secure box. Then, a sample is taken from that box (like, 100 ballots) which are statistically checked against the results. If there's a discrepancy, then something went wrong. The printout would take precedence over the electronic results in the cases of discrepancies being found, a tight race requiring a recount, etc.
With that scheme, there are a few possible problems:
1. The printer could fail, stopping voting at that location or in that booth.
2. The user could fail to take, to verify, or to leave one copy of their voting.
3. Someone could tamper with the contents of the box.
4. Someone could tamper with the sampling of the contents of the box.
I think those four (there might be more) are manageable. Much more so than trying to ensure that the software and the hardware is secure.