Republican lawmakers are moving quickly to try and allow states to require proof of citizenship for a voter registration form after the Supreme Court rejected an Arizona law that did just that.

In a blow to Arizona's efforts to toughen its voter ID standards, the high court on Monday ruled 7-2 that states could not unilaterally require would-be voters to prove citizenship in order to use a federal registration form. The court ruled that because the federal "Motor Voter" registration law -- which created the form -- doesn't require that documentation, Arizona could not on its own demand it.

In response, Sens. Ted Cruz, R-Texas, and David Vitter, R-La., announced an amendment to the Senate immigration overhaul that would explicitly allow states to impose those requirements.

In a statement, Cruz said the Supreme Court ruling leaves a "hole in federal law" that must be addressed.
"This encourages voter fraud and we must ensure that our elections are fair and accurately reflect the will of our citizens," he said.

The amendment would adjust the federal law so that states would be able to require proof of citizenship in order to complete any federal voter registration form.