I Googled it. The law you refer to was overturned by the Missouri state supreme court. I noted this sentence in the article:
Originally Posted by Dion
Hearne also was involved in Indiana's voter ID law, which the U.S. Supreme Court upheld in 2008 against claims that it infringed on rights guaranteed under the U.S. Constitution.
That led me to this:
Supreme Court Decides Challenge to State Voter Identification Laws
In April 2008, the Supreme Court decided a case challenging Indiana's strict voter identification law. In Crawford v Marion Election Board, the Court considered an appeal from a Seventh Circuit decision upholding a Indiana law that required voters to present either a driver's license, a passport, or a state-issued photo identification card. In a 2 to 1 panel decision, Judge Richard Posner found the law not to violate the First Amendment or the Equal Protection Clause. Posner wrote, "It is exceedingly difficult to manuever in today's America without a photo id (try flying, or even entering a tall building, such as the courthouse in which we sit, without one). And, as a consequence, a vast majority of adults have such identification." A 2007 study showed that 13% of registered voters in Indiana lacked the required identification and that most of those tend to vote Democratic. (The law disproportionately affects the poor, minorities, and the elderly, who usually vote for Democrats.) The Bush administration took the side of Indiana, arguing in an amicus brief that the state has an interest in "deterring voter fraud."
By a vote of 6 to 3, the Court rejected the challenge. Three justices (Stevens, Roberts, and Kennedy) allowed that an as-applied challenge to the law might have merit if a plaintiff could show that the law placed a special "burden" on his or her ability to vote, such that heightened scrutiny of the law was appropriate. Three concurring justices (Scalia, Thomas, and Alito) believed that the Indiana law should be subjected only to rational basis analysis, and that the state's interest in preventing voter fraud constituted a rational basis.
Three dissenting justices (Souter, Ginsburg, and Breyer) concluded, using a balancing test, that Indiana's interest in preventing voter fraud did not justify the significant burden the law placed on specific groups of voters.
The argument pressed by the plaintiffs that any burden on the right to vote, however slight it is or however meager the number of voters affected by it, cannot pass constitutional muster unless it is shown to serve a compelling state interest was rejected in Burdick v. Takushi and rejected again in Crawford. In Takushi the Court said, "Election laws will invariably impose some burden upon individual voters. . . . [T]o subject every voting regulation to strict scrutiny and to require that the regulation be narrowly tailored to advance a compelling state interest, as petitioner suggests, would tie the hands of States seeking to assure that elections are operated equitably and efficiently."
My interpretation is that voter ID requirements are Constitutional.