Just hours after the Supreme Court ruled that federal law pre-empted Arizona from requiring proof of citizenship to register to vote, Sen. Ted Cruz said he would try to change that.

The Texas Republican made the announcement on Twitter:

I'll file amendment to immigration bill that permits states to require ID before registering voters & close this hole in fed statutory law.

— Senator Ted Cruz (@SenTedCruz) June 17, 2013

Majority Leader Harry Reid on Monday reiterated his threat of a weekend session to process amendments.

“I know many of my colleagues have ideas about how to improve this bill. I hope we will be able to process additional amendments soon, so that we can give those ideas the debate and the votes they deserve. We have five amendments pending. We could vote on four of them right away,” the Nevada Democrat said. “My colleagues should be aware, unless we begin voting on amendments soon, we will need to work through the weekend in order to finish this bill before July 4.”

As our colleague David Hawkings explained earlier today, the Supreme Court struck down Arizona’s Proposition 200, which requires prospective Arizona voters to demonstrate that they are U.S. citizens.

In his majority opinion, Justice Antonin Scalia explained that while Arizona’s law is pre-empted by federal statue, the state could use a different method to try to establish “state-specific instructions” on the the Election Assistance Commission’s federal voter registration form, with a legal process for review in the event the EAC opposes the state’s proposal.

That alternative means of enforcing its constitutional power to determine voting qualifications remains open to Arizona here. Should the EAC reject or decline to act on a renewed request, Arizona would have the opportunity to establish in a reviewing court that a mere oath will not suffice to effectuate its citizenship requirement and that the EAC is therefore under a nondiscretionary duty to include Arizona’s concrete-evidence requirement on the Federal Form.