Republican lawmakers in North Carolina completed an override of Democratic Gov. Roy Cooper’s veto of a new voter ID law this week -- and immediately faced a challenge in court.

Six voters described as either black or biracial residents filed the lawsuit Wednesday, mere minutes after the state House voted to override the veto 72-40. The state Senate had voted to override Tuesday, the News & Observer of Raleigh reported.

Republicans have blasted Cooper, who last week had said no to the legislation even though more than 55 percent of the state’s voters had approved it in a recent referendum.

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"You have betrayed the majority of the hard-working, honest people of North Carolina who put this provision into our constitution," Republican state Rep. Jimmy Dixon said of Cooper. "You should hang your head in shame."

"You have betrayed the majority of the hard-working, honest people of North Carolina who put this provision into our constitution. You should hang your head in shame." — State Rep. Jimmy Dixon

The referendum called for the state’s constitution to add an amendment requiring in-person voter photo ID, expanding the number of qualifying forms of ID and exceptions compared to legislation blocked earlier this decade. Republicans say the changes will ensure that everyone lawfully registered to vote can cast a ballot.

Permitted IDs would include traditional driver's licenses and military identification, student IDs from colleges and universities, and employee ID cards for state and local governments. Those IDs must meet certain security thresholds.

The voters who filed the lawsuit Wednesday said the restrictions will disproportionately and unduly burden the right to vote for African-American and American Indian residents. The suit claims the bill will add a financial cost to voting in the form of lost work hours and the need to find transportation to obtain an ID.

State Democrats have said the law was meant to suppress votes.

“You don’t have a right to take away my right or anybody else’s right because they can’t supply you with a photo ID,” Democratic state Rep. Mickey Michaux told the News & Observer. “It looks like history is going to repeat itself.”

But Republicans rebuffed such claims, saying Democrats were responsible for slavery and Jim Crow, the paper reported.

“The Republicans are the party of emancipation,” Republican state Rep. Jeff Collins said. “I get tired of getting blamed for things the Democrats have done.”

“The Republicans are the party of emancipation. I get tired of getting blamed for things the Democrats have done.” — State Rep. Jeff Collins

The lawsuit also asks that a three-judge panel of state judges prevent the law from being enforced during the litigation. Any appeals would go to the state Supreme Court.

Fox News’ Dom Calicchio and the Associated Press contributed to this report.