I invite you to peruse the CONSTITUTION.
http://www.usconstitution.net/const.html
Article II states:
In taking upon itself the interpretation of a law in such a way as to take away the States' right to direct their own elections, the 9th Circus has removed this Constitutional protection and quite literally is forcing the States to accept illegal aliens as valid voters to select its electors AND it's state elected positions. Where in the Constitution does the Federal government gain the power to override the Tenth Amendment and dictate this to the States?
Previous expansions of voting rights required Amendments. Now the 9th Circus has determined that enfranchising illegal aliens is such a pressing national need that the Constitution can be dispensed with entirely.
Note also that there is absolutely noting in the section you quoted which says the States may not ask for verification of citizenship. It merely that States must offer the ability to register to vote at the same time one applies for a driver's license, it does NOT state that the requirements to vote must be the same as those to receive a driver's license. Since citizenship is required to vote but not required to receive a driver's license, it has been understood for seventeen years that the two have different requirements. But now the Clowns in Gowns have once again stepped forward to trash the Constitution in favor of rule by magistrates appointed for life.