Cruz’s legislation was prompted by a Supreme Court ruling, Arizona v. Inter Tribal Council of Arizona, Inc., where it decided that the National Voter Registration Act pre-empted Arizona’s requirement that a person present proof of citizenship before they are allowed to register to vote.

Cruz said the court decision “undermines” fair elections and “encourages voter fraud” by allowing noncitizens to register without showing proof of citizenship. 

Democrats argue that there isn’t proof illegal immigrants are trying to commit voter fraud.

Republican Sens. David VitterDavid VitterOvernight Energy: Trump set to propose sharp cuts to EPA, energy spending Former La. official tapped as lead offshore drilling regulator Former senator who crafted chemicals law to lobby for chemicals industry MORE (La.), Mike LeeMike LeeMcConnell courts GOP centrists for health bill Rand Paul calls to slow down 'rushed' ObamaCare repeal process GOP hits the gas on ObamaCare repeal MORE (Utah), John CornynJohn CornynThe Hill's 12:30 Report Five things to watch in Senate GOP’s ObamaCare repeal bill McConnell courts GOP centrists for health bill MORE (Texas), Tom CoburnTom Coburn'Path of least resistance' problematic for Congress Freedom Caucus saved Paul Ryan's job: GOP has promises to keep Don't be fooled: Carper and Norton don't fight for DC MORE (Okla.), Thad CochranThad CochranDefense hawks gird for budget brawl Congressional politics hurts cotton farmers GOP senators dismiss Trump filibuster change MORE (Miss.), Mike CrapoMike CrapoSenate overwhelmingly passes Russia sanctions deal Russia sanctions deal clears key Senate hurdle Treasury finally releases reform plan, but Senate snafu awaits MORE (Idaho), Jeff SessionsJeff SessionsGingrich: Media was right, special elections were a referendum Overnight Regulation: Labor groups fear rollback of Obama worker protection rule | Trump regs czar advances in Senate | New FCC enforcement chief Overnight Tech: Uber CEO resigns | Trump's Iowa tech trip | Dems push Sessions to block AT&T-Time Warner deal | Lawmakers warned on threat to election systems | MORE (Ala.), Ron JohnsonRon JohnsonGOP senator: I would not call this 'ObamaCare repeal' Live coverage: Senate GOP unveils its ObamaCare repeal bill Rand Paul calls to slow down 'rushed' ObamaCare repeal process MORE (Wis.) and Jim RischJim RischFive questions after Comey’s testimony Comey delivers dramatic rebuke of Trump Trump, GOP plot path for agenda MORE (Idaho) are cosponsoring the bill, S. 1336.

Cruz said he tried to add the bill’s language to the immigration reform legislation passed last month, but he was unable to get a vote on the amendment.