To massively generalize, in America today Republicans are mostly conservatives, and conservatives find their base in the rural populations and split the suburbs with Democrats because people in the middle class under pressure will tend to revert to conservative values. Democrats are mostly liberals, and liberals find their base in urban populations and that portion of the suburbs which feels confident enough to be able to pay to support government programs.

The reason I just massively generalized is because in modern voting cycles, voter fraud manifested in the form of ballot-box stuffing is most easily conducted in urban areas by individuals with poor or no ID credentials - the homeless, the indigent, and other people who are transient for one reason or another (e.g., students). These people tend to vote Democratic.

As a result, any attempt to force ID cards is opposed by Democrats, who see in such attempts a manifestation of a historic conservative form of voter fraud, namely, denial of voting rights. Of course, this was historically conducted by white Democrats, but at the time conservatives in the South were Democrats because it was the Republicans who "invaded" under Lincoln. The Jim Crow laws were part and parcel of a wider social scheme to keep blacks disenfranchised, outside of political and socioeconomic power structures and marginalized in society generally.

Democrats like to play down the risk of voter fraud, but groups investigating the 2008 election (and even more so, the 2008 Democratic primary) have uncovered evidence of massive voter fraud in the form of ballot-box stuffing. Whether the evidence is merely the "tip of the iceberg" as Republicans claim or an "exaggeration" as Democrats claim, is an argument that can go on for years.

However, my personal opinion is that ballot-box stuffing is a significant and serious risk, and there are enough "get out the vote" and "voter registration" type organizations out there that can help ensure that everyone gets an ID card. It is easy enough to implement and maintain, and not an unbearable burden. It increases faith in the electoral system and that is a good thing. It decreases the ability of people to delegitimize an election on the grounds that "the dead voted", or that officials cast ballots for people on voter lists who didn't show up.