House Speaker Davy Carter, R-Cabot, didn't vote on the measure and declined Wednesday to say whether he'd support overriding Beebe's veto.
"I'm going to go back and read the (attorney general's) opinion and the governor's reasoning on why he vetoed the bill," he told reporters. "Fundamentally I think we're down to the reasoning behind the veto, so I'll look at that and see."
The bill would exempt voters who live in nursing homes and other long-term care facilities.
Beebe said Monday he was vetoing the bill because voter fraud hasn't been shown to be a problem.
"At a time when some argue for the reduction of unnecessary bureaucracy and for reduced government spending, I find it ironic to be presented with a bill that increases government bureaucracy and increases government expenditures, all to address a need that has not been demonstrated," Beebe wrote in his veto letter. "I cannot approve such an unnecessary measure that would negatively impact one of our most precious rights as citizens."
Associated Press Writer Michael Stratford contributed to this report
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