Nebraska state senators voted 31-15 on Wednesday to restore the program, which was eliminated two years ago after providing prenatal care for decades.

The number of votes in favor was one more than would be needed to override the veto and the Nebraska legislature has one day left in its current session -- next Wednesday -- in which to do so.

"I oppose providing taxpayer benefits to illegal immigrants," Heineman said in his veto letter.

Heineman, who is anti-abortion, also said he had "grave concerns" that some funding could go to abortion provider Planned Parenthood and that Nebraska could become a sanctuary for illegal immigrants because no bordering states offered similar coverage.

About 1,600 low-income women were affected when Nebraska eliminated the program in 2010. About half were illegal immigrants and others were women who lost benefits for failing to comply with all requirements. Coverage was later restored for legal residents and others who do not qualify for Medicaid.

Religious, anti-abortion and health groups have called on Nebraska to restore the coverage, saying it was morally right and fiscally prudent. The state must pay for birth defects and other complications suffered by children who are U.S. citizens upon birth and qualify for taxpayer-funded health care.

Restoring the program would cost about $650,000 in state funds, plus $1.9 million in federal money annually. The tax-funded care has been estimated at $1,500 to $2,000 per mother.

Supporters of the bill have said the $650,000 cost is less than the $800,000 medical bill for one child - paid by Nebraska taxpayers - whose health problems were caused by the lack of prenatal care for an immigrant mother in one case since 2010.

(Reporting by David Bailey; Editing by David Brunnstrom)

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