It's not the showing of an ID, but getting an ID that will be a hurdle to a lot of people. The new laws are going to apparently affect mostly non-republican oriented voters ...
See for example : http://www.veteransnewsnow.com/2012/07/18/wisconsin-gop-voter-obstruction-act-23-permanently-halted-by-judge/
or even more obvious
Voter ID is there to protect the citizens from someone voting under their name. No, it is not a widespread, documented problem, but it is a possibility that it can happen, and it does happen. I am originally from Mississippi. There have been several instances of dead people voting. Before I moved to Germany in 2010, all I had to do to vote was to walk up to the table in my voting precinct, tell the person my name, say yes when they read me the address next to my name, take my ballot and go into the booth. So, there was nothing to stop a person from claiming to be me and voting for John McCain in the last election. Now, if I went to vote and was told that I had already voted, then I could correct the problem after a lot of paperwork etc. Also, if a person has died recently, a person could claim to be that person and vote as long as they new the address. This type of information is publicly available. If two of the people at the voting place know that the person is indeed deceased, this can be prevented. But if no one knows, then there is nothing to stop the fraud.
Everyone that has any sort of interaction with the government must have a picture ID. Most of the poor in America have interaction with the government for their social assistance. All of these people already have a picture ID. If a person has a bank account, they have a picture ID. Unless they opened it many years ago. Sure, some people will have to get a friend or relative to take them to the local courthouse that is in each county in order to get one, that is not a big deal to most. The ID is free in all states to those that need one. The only time a person is required to pay for a voter ID is if they already possess a state issued voter ID- drivers license, school ID etc. These people do not need a new ID, they already have one. If they want an extra ID, then they can pay for it.
I can not think of any real reason not to require a person to prove that they are 1. a citizen that has the right to vote. and 2. that they are indeed the person they say that they are. Why would a person not want to show an ID? The moment that they are asked to show the ID comes when they are physically standing in the voting place (everyone can see them walk in and out) and after they have already stated their name (the people in the immediate vicinity can hear this) so the person's identity is not a logical issue, therefore voter intimidation is not the issue.
So, again, why would a person not want to show a photo ID? Why would a person not want there to be a mechanism in place to prevent someone from casting your (or your deceased family member's) vote?