The registered democrats should be required to show a picture ID, and the registered republicans should be required to show their american express card

j/k
Seriously, there are politicians out there that pander to the poor. They make lots of promises to the poor, saying that we will take care of you or we will give you all kinds of stuff for free or we will raise taxes on the rich and spend it all on the you. They typically all have the same party affiliation.
Those politicians are the ones who would prefer to let people without IDs vote because they will probably vote for them. They don't care if it's fraud as long as they win.
Loretta Sanchez, dianne feinstein, and Barbara Boxter all come to mind as examples but there are hundreds of others.
Now, politicians that belong to the "other " political party would probably do it too, except they know that the poor probably won't vote for them. That's because they promise to make people earn they own money and then let them keep a large percentage of it. Poor people don't like that. They want what someone else has so they vote for people who will take it away from the other guy and give it to them.
IMO A legal government-issued ID should be required to register to vote also. in fact it should be required to do anything in this country that remotely has to do with the government, including collecting benefits, getting medical care, and enrolling children in public schools.